<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c7">o</font>, <font color="Maroon" title="c8">p</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">r</font> being <a href="xxreal_0.html#V2" title="XXREAL_0:attr.2">positive</a> <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>   st <font color="Maroon" title="c8">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topreal9.html#K1" title="TOPREAL9:func.1">Ball</a> <font color="Maroon" title="c7">o</font>,<font color="Olive" title="b1">r</font> holds <br/> <a href="jordan.html#K10" title="JORDAN:func.10">RotateCircle</a> <font color="Maroon" title="c7">o</font>,<font color="Olive" title="b1">r</font>,<font color="Maroon" title="c8">p</font> is <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a></span><br/><b>let </b><font color="Maroon" title="c9">r</font> be  <a href="xxreal_0.html#V2" title="XXREAL_0:attr.2">positive</a> <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c8">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topreal9.html#K1" title="TOPREAL9:func.1">Ball</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font> implies  <a href="jordan.html#K10" title="JORDAN:func.10">RotateCircle</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c8">p</font> is <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a> )</span><br/>



<b>assume </b><a NAME="E1:98"/><i><font color="Green" title="E72">A1</font></i>: 
<font color="Maroon" title="c8">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topreal9.html#K1" title="TOPREAL9:func.1">Ball</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="jordan.html#K10" title="JORDAN:func.10">RotateCircle</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c8">p</font> is <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a></span><br/>

<b>set </b><font color="Maroon" title="c10">D</font> =  <a href="brouwer.html#K2" title="BROUWER:func.2">Tdisk</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font>;<br/>
<b>set </b><font color="Maroon" title="c11">cB</font> =  <a href="topreal9.html#K2" title="TOPREAL9:func.2">cl_Ball</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font>;<br/>
<b>set </b><font color="Maroon" title="c12">Bp</font> =  <a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font>;<br/>
<b>set </b><font color="Maroon" title="c13">OK</font> = <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span>;<br/>
<b>set </b><font color="Maroon" title="c14">D1</font> = <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>;<br/>
<b>set </b><font color="Maroon" title="c15">D2</font> = <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p1">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c16">S1</font> =  <a href="toprealb.html#K7" title="TOPREALB:func.7">Tcircle</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font>;<br/>
<a NAME="E2:98"/><i><font color="Green" title="E73">A2</font></i>: 
<span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p1">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="toprealb.html#K7" title="TOPREALB:func.7">Tcircle</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font>
 
<b>by </b><i><a class="ref" href="toprealb.html#D6" title="TOPREALB:def.6">TOPREALB:def 6</a></i>;<br/>
<a NAME="E3:98"/><i><font color="Green" title="E74">A3</font></i>: 
 <a href="topreal9.html#K1" title="TOPREAL9:func.1">Ball</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font> <a href="subset_1.html#R1" title="SUBSET_1:pred.1">misses</a>  <a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font>
 
<b>by </b><i><a class="ref" href="topreal9.html#T19" title="TOPREAL9:th.19">TOPREAL9:19</a></i>;<br/>
<a NAME="E4:98"/><i><font color="Green" title="E75">A4</font></i>: 
<font color="Maroon" title="c8">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E5:98"/><i><font color="Green" title="E76">A5</font></i>: 
 <a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="topreal9.html#K2" title="TOPREAL9:func.2">cl_Ball</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font>
 
<b>by </b><i><a class="ref" href="topreal9.html#T17" title="TOPREAL9:th.17">TOPREAL9:17</a></i>;<br/>
<a NAME="E6:98"/><i><font color="Green" title="E77">A6</font></i>: 
 <a href="topreal9.html#K1" title="TOPREAL9:func.1">Ball</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="topreal9.html#K2" title="TOPREAL9:func.2">cl_Ball</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font>
 
<b>by </b><i><a class="ref" href="topreal9.html#T16" title="TOPREAL9:th.16">TOPREAL9:16</a></i>;<br/>
<a NAME="E7:98"/><i><font color="Green" title="E78">A7</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="brouwer.html#K2" title="BROUWER:func.2">Tdisk</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topreal9.html#K2" title="TOPREAL9:func.2">cl_Ball</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font>
 
<b>by </b><i><a class="ref" href="brouwer.html#T3" title="BROUWER:th.3">BROUWER:3</a></i>;<br/>
<a NAME="E8:98"/><i><font color="Green" title="E79">A8</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<b>by </b><i><a class="ref" href="pre_topc.html#T29" title="PRE_TOPC:th.29">PRE_TOPC:29</a></i>;<br/>
<a NAME="E9:98"/><i><font color="Green" title="E80">A9</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font>
 
<b>by </b><i><a class="ref" href="pre_topc.html#T29" title="PRE_TOPC:th.29">PRE_TOPC:29</a></i>;<br/>
<b>set </b><font color="Maroon" title="c17">TD</font> = <span class="p1"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span>;<br/>
<b>set </b><font color="Maroon" title="c18">gg</font> =  <a href="jordan.html#K10" title="JORDAN:func.10">RotateCircle</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c8">p</font>;<br/>
<b>set </b><font color="Maroon" title="c19">xo</font> =  <a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font>;<br/>
<b>set </b><font color="Maroon" title="c20">yo</font> =  <a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font>;<br/>
<b>set </b><font color="Maroon" title="c21">dx</font> =  <a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a> ;<br/>
<b>set </b><font color="Maroon" title="c22">dy</font> =  <a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a> ;<br/>
<b>set </b><font color="Maroon" title="c23">fx2</font> =  <a href="jordan.html#K7" title="JORDAN:func.7">Proj2_1</a> ;<br/>
<b>set </b><font color="Maroon" title="c24">fy2</font> =  <a href="jordan.html#K8" title="JORDAN:func.8">Proj2_2</a> ;<br/>
<b>reconsider </b><font color="Maroon" title="c25">rr</font> = <font color="Maroon" title="c9">r</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a>  as   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> <b>by </b><i><a class="ref" href="xreal_0.html#D1" title="XREAL_0:def.1">XREAL_0:def 1</a></i>;<br/>
<b>set </b><font color="Maroon" title="c26">f1</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <font color="Maroon" title="c25">rr</font>;<br/>
<b>reconsider </b><font color="Maroon" title="c27">f1</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <font color="Maroon" title="c25">rr</font> as  <a href="pscomp_1.html#V9" title="PSCOMP_1:attr.9">continuous</a> <a href="pscomp_1.html#NM1" title="PSCOMP_1:NM.1">RealMap</a> of <span class="p1"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span> <b>by </b><i><a class="txt" href="jordan.html#E21"><i><font color="Green" title="E16">Lm8</font></i></a></i>;<br/>
<b>set </b><font color="Maroon" title="c28">Zf1</font> = <font color="Maroon" title="c27">f1</font> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span>;<br/>
<b>set </b><font color="Maroon" title="c29">Zfx2</font> = <a href="jordan.html#K7" title="JORDAN:func.7">Proj2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span>;<br/>
<b>set </b><font color="Maroon" title="c30">Zfy2</font> = <a href="jordan.html#K8" title="JORDAN:func.8">Proj2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span>;<br/>
<b>set </b><font color="Maroon" title="c31">Zdx</font> = <a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span>;<br/>
<b>set </b><font color="Maroon" title="c32">Zdy</font> = <a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span>;<br/>
<b>set </b><font color="Maroon" title="c33">Zxo</font> = <span class="p1">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span>;<br/>
<b>set </b><font color="Maroon" title="c34">Zyo</font> = <span class="p1">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span>;<br/>
<b>set </b><font color="Maroon" title="c35">xx</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p1">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c36">yy</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p1">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c37">m</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span>;<br/>
<a NAME="E12:98"/><i><font color="Green" title="E81">A10</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span>
 
<b>by </b><i><a class="ref" href="pre_topc.html#T29" title="PRE_TOPC:th.29">PRE_TOPC:29</a></i>;<br/>
<a NAME="E13:98"/><i><font color="Green" title="E82">A11</font></i>: 
for <font color="Olive" title="b1">y</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span><br/> for <font color="Olive" title="b2">z</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span>)</span> holds  <span class="p1">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Olive" title="b1">y</font>,<font color="Olive" title="b2">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Olive" title="b1">y</font>,<font color="Olive" title="b2">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="98_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c38">y</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">z</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span>)</span> holds  <span class="p1">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c38">y</font>,<font color="Olive" title="b1">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c38">y</font>,<font color="Olive" title="b1">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span><br/><b>let </b><font color="Maroon" title="c39">z</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c38">y</font>,<font color="Maroon" title="c39">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c38">y</font>,<font color="Maroon" title="c39">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span><br/>



<a NAME="E1:98_1"/>
<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c38">y</font>,<font color="Maroon" title="c39">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span>
 
<b>by </b><i><a class="txt" href="#E8:98"><i><font color="Green" title="E79">A8</font></i></a>, <a class="txt" href="#E9:98"><i><font color="Green" title="E80">A9</font></i></a>, <a class="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</a></i>;<br/>
<b>hence </b><a NAME="E2:98_1"/>
<span class="p1">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c38">y</font>,<font color="Maroon" title="c39">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c38">y</font>,<font color="Maroon" title="c39">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>
 <b>by </b><i><a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E14:98"/><i><font color="Green" title="E83">A12</font></i>: 
for <font color="Olive" title="b1">y</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span><br/> for <font color="Olive" title="b2">z</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span>)</span> holds  <span class="p1">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Olive" title="b1">y</font>,<font color="Olive" title="b2">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Olive" title="b1">y</font>,<font color="Olive" title="b2">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="98_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c38">y</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">z</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span>)</span> holds  <span class="p1">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c38">y</font>,<font color="Olive" title="b1">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c38">y</font>,<font color="Olive" title="b1">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span><br/><b>let </b><font color="Maroon" title="c39">z</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c38">y</font>,<font color="Maroon" title="c39">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c38">y</font>,<font color="Maroon" title="c39">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span><br/>



<a NAME="E1:98_2"/>
<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c38">y</font>,<font color="Maroon" title="c39">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span>
 
<b>by </b><i><a class="txt" href="#E8:98"><i><font color="Green" title="E79">A8</font></i></a>, <a class="txt" href="#E9:98"><i><font color="Green" title="E80">A9</font></i></a>, <a class="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</a></i>;<br/>
<b>hence </b><a NAME="E2:98_2"/>
<span class="p1">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c38">y</font>,<font color="Maroon" title="c39">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c38">y</font>,<font color="Maroon" title="c39">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>
 <b>by </b><i><a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E15:98"/><i><font color="Green" title="E84">A13</font></i>: 
for <font color="Olive" title="b1">y</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span><br/> for <font color="Olive" title="b2">z</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span>)</span> holds  <span class="p1">(<span class="default"><a href="jordan.html#K7" title="JORDAN:func.7">Proj2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Olive" title="b1">y</font>,<font color="Olive" title="b2">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="jordan.html#K7" title="JORDAN:func.7">Proj2_1</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Olive" title="b1">y</font>,<font color="Olive" title="b2">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="98_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c38">y</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">z</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span>)</span> holds  <span class="p1">(<span class="default"><a href="jordan.html#K7" title="JORDAN:func.7">Proj2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c38">y</font>,<font color="Olive" title="b1">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="jordan.html#K7" title="JORDAN:func.7">Proj2_1</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c38">y</font>,<font color="Olive" title="b1">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span><br/><b>let </b><font color="Maroon" title="c39">z</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="jordan.html#K7" title="JORDAN:func.7">Proj2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c38">y</font>,<font color="Maroon" title="c39">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="jordan.html#K7" title="JORDAN:func.7">Proj2_1</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c38">y</font>,<font color="Maroon" title="c39">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span><br/>



<a NAME="E1:98_3"/>
<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c38">y</font>,<font color="Maroon" title="c39">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span>
 
<b>by </b><i><a class="txt" href="#E8:98"><i><font color="Green" title="E79">A8</font></i></a>, <a class="txt" href="#E9:98"><i><font color="Green" title="E80">A9</font></i></a>, <a class="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</a></i>;<br/>
<b>hence </b><a NAME="E2:98_3"/>
<span class="p1">(<span class="default"><a href="jordan.html#K7" title="JORDAN:func.7">Proj2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c38">y</font>,<font color="Maroon" title="c39">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="jordan.html#K7" title="JORDAN:func.7">Proj2_1</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c38">y</font>,<font color="Maroon" title="c39">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>
 <b>by </b><i><a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E16:98"/><i><font color="Green" title="E85">A14</font></i>: 
for <font color="Olive" title="b1">y</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span><br/> for <font color="Olive" title="b2">z</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span>)</span> holds  <span class="p1">(<span class="default"><a href="jordan.html#K8" title="JORDAN:func.8">Proj2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Olive" title="b1">y</font>,<font color="Olive" title="b2">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="jordan.html#K8" title="JORDAN:func.8">Proj2_2</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Olive" title="b1">y</font>,<font color="Olive" title="b2">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="98_4"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c38">y</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">z</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span>)</span> holds  <span class="p1">(<span class="default"><a href="jordan.html#K8" title="JORDAN:func.8">Proj2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c38">y</font>,<font color="Olive" title="b1">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="jordan.html#K8" title="JORDAN:func.8">Proj2_2</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c38">y</font>,<font color="Olive" title="b1">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span><br/><b>let </b><font color="Maroon" title="c39">z</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="jordan.html#K8" title="JORDAN:func.8">Proj2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c38">y</font>,<font color="Maroon" title="c39">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="jordan.html#K8" title="JORDAN:func.8">Proj2_2</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c38">y</font>,<font color="Maroon" title="c39">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span><br/>



<a NAME="E1:98_4"/>
<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c38">y</font>,<font color="Maroon" title="c39">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span>
 
<b>by </b><i><a class="txt" href="#E8:98"><i><font color="Green" title="E79">A8</font></i></a>, <a class="txt" href="#E9:98"><i><font color="Green" title="E80">A9</font></i></a>, <a class="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</a></i>;<br/>
<b>hence </b><a NAME="E2:98_4"/>
<span class="p1">(<span class="default"><a href="jordan.html#K8" title="JORDAN:func.8">Proj2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c38">y</font>,<font color="Maroon" title="c39">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="jordan.html#K8" title="JORDAN:func.8">Proj2_2</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c38">y</font>,<font color="Maroon" title="c39">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>
 <b>by </b><i><a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E17:98"/><i><font color="Green" title="E86">A15</font></i>: 
for <font color="Olive" title="b1">y</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span><br/> for <font color="Olive" title="b2">z</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span>)</span> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c27">f1</font> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Olive" title="b1">y</font>,<font color="Olive" title="b2">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c27">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Olive" title="b1">y</font>,<font color="Olive" title="b2">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="98_5"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c38">y</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">z</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span>)</span> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c27">f1</font> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c38">y</font>,<font color="Olive" title="b1">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c27">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c38">y</font>,<font color="Olive" title="b1">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span><br/><b>let </b><font color="Maroon" title="c39">z</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c27">f1</font> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c38">y</font>,<font color="Maroon" title="c39">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c27">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c38">y</font>,<font color="Maroon" title="c39">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span><br/>



<a NAME="E1:98_5"/>
<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c38">y</font>,<font color="Maroon" title="c39">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span>
 
<b>by </b><i><a class="txt" href="#E8:98"><i><font color="Green" title="E79">A8</font></i></a>, <a class="txt" href="#E9:98"><i><font color="Green" title="E80">A9</font></i></a>, <a class="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</a></i>;<br/>
<b>hence </b><a NAME="E2:98_5"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c27">f1</font> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c38">y</font>,<font color="Maroon" title="c39">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c27">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c38">y</font>,<font color="Maroon" title="c39">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>
 <b>by </b><i><a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E18:98"/><i><font color="Green" title="E87">A16</font></i>: 
for <font color="Olive" title="b1">y</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span><br/> for <font color="Olive" title="b2">z</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span>)</span> holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Olive" title="b1">y</font>,<font color="Olive" title="b2">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Olive" title="b1">y</font>,<font color="Olive" title="b2">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="98_6"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c38">y</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">z</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span>)</span> holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c38">y</font>,<font color="Olive" title="b1">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c38">y</font>,<font color="Olive" title="b1">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span><br/><b>let </b><font color="Maroon" title="c39">z</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c38">y</font>,<font color="Maroon" title="c39">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c38">y</font>,<font color="Maroon" title="c39">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span><br/>



<a NAME="E1:98_6"/>
<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c38">y</font>,<font color="Maroon" title="c39">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span>
 
<b>by </b><i><a class="txt" href="#E8:98"><i><font color="Green" title="E79">A8</font></i></a>, <a class="txt" href="#E9:98"><i><font color="Green" title="E80">A9</font></i></a>, <a class="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</a></i>;<br/>
<b>hence </b><a NAME="E2:98_6"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c38">y</font>,<font color="Maroon" title="c39">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c38">y</font>,<font color="Maroon" title="c39">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>
 <b>by </b><i><a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E19:98"/><i><font color="Green" title="E88">A17</font></i>: 
for <font color="Olive" title="b1">y</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span><br/> for <font color="Olive" title="b2">z</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span>)</span> holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Olive" title="b1">y</font>,<font color="Olive" title="b2">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Olive" title="b1">y</font>,<font color="Olive" title="b2">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="98_7"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c38">y</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">z</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span>)</span> holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c38">y</font>,<font color="Olive" title="b1">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c38">y</font>,<font color="Olive" title="b1">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span><br/><b>let </b><font color="Maroon" title="c39">z</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c38">y</font>,<font color="Maroon" title="c39">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c38">y</font>,<font color="Maroon" title="c39">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span><br/>



<a NAME="E1:98_7"/>
<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c38">y</font>,<font color="Maroon" title="c39">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span>
 
<b>by </b><i><a class="txt" href="#E8:98"><i><font color="Green" title="E79">A8</font></i></a>, <a class="txt" href="#E9:98"><i><font color="Green" title="E80">A9</font></i></a>, <a class="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</a></i>;<br/>
<b>hence </b><a NAME="E2:98_7"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c38">y</font>,<font color="Maroon" title="c39">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c38">y</font>,<font color="Maroon" title="c39">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>
 <b>by </b><i><a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="98_8"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c38">b</font> be  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c38">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span> implies  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c38">b</font> )</span><br/><b>assume </b><a NAME="E1:98_8"/>
<font color="Maroon" title="c38">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c38">b</font></span><br/><b>then consider </b><font color="Maroon" title="c39">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:98_8"/><i><font color="Green" title="E89">A18</font></i>: 
<font color="Maroon" title="c39">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E4:98_8"/><i><font color="Green" title="E90">A19</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c39">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c38">b</font>
 <b>by </b><i><a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/><b>consider </b><font color="Maroon" title="c40">y</font>, <font color="Maroon" title="c41">z</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E6:98_8"/><i><font color="Green" title="E91">A20</font></i>: 
( <font color="Maroon" title="c40">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp; <font color="Maroon" title="c41">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font> &amp; <font color="Maroon" title="c39">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c40">y</font>,<font color="Maroon" title="c41">z</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> )
 <b>by </b><i><a class="txt" href="#E12:98"><i><font color="Green" title="E81">A10</font></i></a>, <a class="txt" href="#E3:98_8"><i><font color="Green" title="E89">A18</font></i></a>, <a class="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</a></i>;<br/><a NAME="E7:98_8"/><i><font color="Green" title="E92">A21</font></i>: 
<font color="Maroon" title="c40">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">p</font>
 <b>by </b><i><a class="txt" href="#E6:98_8"><i><font color="Green" title="E91">A20</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c42">y</font> = <font color="Maroon" title="c40">y</font>, <font color="Maroon" title="c43">z</font> = <font color="Maroon" title="c41">z</font> as   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <b>by </b><i><a class="txt" href="#E6:98_8"><i><font color="Green" title="E91">A20</font></i></a></i>;<br/><a NAME="E9:98_8"/><i><font color="Green" title="E93">A22</font></i>: 
<font color="Maroon" title="c42">y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c43">z</font>
 <b>by </b><i><a class="txt" href="#E1:98"><i><font color="Green" title="E72">A1</font></i></a>, <a class="txt" href="#E3:98"><i><font color="Green" title="E74">A3</font></i></a>, <a class="txt" href="#E6:98_8"><i><font color="Green" title="E91">A20</font></i></a>, <a class="txt" href="#E7:98_8"><i><font color="Green" title="E92">A21</font></i></a>, <a class="ref" href="xboole_0.html#T3" title="XBOOLE_0:th.3">XBOOLE_0:3</a></i>;<br/><a NAME="E10:98_8"/>
<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c42">y</font>,<font color="Maroon" title="c43">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c42">y</font>,<font color="Maroon" title="c43">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="jordan.html#K1" title="JORDAN:func.1">`1</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c42">y</font>,<font color="Maroon" title="c43">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="jordan.html#K2" title="JORDAN:func.2">`2</a> </span>)</span></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>
 <b>by </b><i><a class="txt" href="jordan.html#E20"><i><font color="Green" title="E15">Lm7</font></i></a>, <a class="ref" href="mcart_1.html#T23" title="MCART_1:th.23">MCART_1:23</a></i>;<br/><a NAME="E11:98_8"/><b>then </b><i><font color="Green" title="E94">A23</font></i>: 
( <font color="Maroon" title="c42">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c42">y</font>,<font color="Maroon" title="c43">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="jordan.html#K1" title="JORDAN:func.1">`1</a>  &amp; <font color="Maroon" title="c43">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c42">y</font>,<font color="Maroon" title="c43">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="jordan.html#K2" title="JORDAN:func.2">`2</a>  )
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></i>;<br/><a NAME="E12:98_8"/><i><font color="Green" title="E95">A24</font></i>: 
<a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c42">y</font>,<font color="Maroon" title="c43">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c42">y</font>,<font color="Maroon" title="c43">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="jordan.html#K1" title="JORDAN:func.1">`1</a> </span>)</span> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c42">y</font>,<font color="Maroon" title="c43">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="jordan.html#K2" title="JORDAN:func.2">`2</a> </span>)</span> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span>
 <b>by </b><i><a class="ref" href="jordan.html#D3" target="_self" title="JORDAN:def.3">Def3</a></i>;<br/><a NAME="E13:98_8"/><i><font color="Green" title="E96">A25</font></i>: 
<a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c42">y</font>,<font color="Maroon" title="c43">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c42">y</font>,<font color="Maroon" title="c43">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="jordan.html#K1" title="JORDAN:func.1">`1</a> </span>)</span> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c42">y</font>,<font color="Maroon" title="c43">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="jordan.html#K2" title="JORDAN:func.2">`2</a> </span>)</span> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span>
 <b>by </b><i><a class="ref" href="jordan.html#D4" target="_self" title="JORDAN:def.4">Def4</a></i>;<br/><b>set </b><font color="Maroon" title="c44">r1</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c42">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c43">z</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span>;<br/><b>set </b><font color="Maroon" title="c45">r2</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c42">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c43">z</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span>;<br/><a NAME="E14:98_8"/><i><font color="Green" title="E97">A26</font></i>: 
<span class="p1">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c42">y</font>,<font color="Maroon" title="c43">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c42">y</font>,<font color="Maroon" title="c43">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>
 <b>by </b><i><a class="txt" href="#E8:98"><i><font color="Green" title="E79">A8</font></i></a>, <a class="txt" href="#E9:98"><i><font color="Green" title="E80">A9</font></i></a>, <a class="txt" href="#E13:98"><i><font color="Green" title="E82">A11</font></i></a>, <a class="txt" href="#E6:98_8"><i><font color="Green" title="E91">A20</font></i></a></i>;<br/><a NAME="E15:98_8"/><i><font color="Green" title="E98">A27</font></i>: 
<span class="p1">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c42">y</font>,<font color="Maroon" title="c43">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c42">y</font>,<font color="Maroon" title="c43">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>
 <b>by </b><i><a class="txt" href="#E8:98"><i><font color="Green" title="E79">A8</font></i></a>, <a class="txt" href="#E9:98"><i><font color="Green" title="E80">A9</font></i></a>, <a class="txt" href="#E14:98"><i><font color="Green" title="E83">A12</font></i></a>, <a class="txt" href="#E6:98_8"><i><font color="Green" title="E91">A20</font></i></a></i>;<br/><i><font color="Green" title="E99">A28</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c42">y</font>,<font color="Maroon" title="c43">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c42">y</font>,<font color="Maroon" title="c43">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c42">y</font>,<font color="Maroon" title="c43">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span>
<b>by </b><i><a class="txt" href="#E3:98_8"><i><font color="Green" title="E89">A18</font></i></a>, <a class="txt" href="#E6:98_8"><i><font color="Green" title="E91">A20</font></i></a>, <a class="ref" href="valued_1.html#T1" title="VALUED_1:th.1">VALUED_1:1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c42">y</font>,<font color="Maroon" title="c43">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c42">y</font>,<font color="Maroon" title="c43">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c42">y</font>,<font color="Maroon" title="c43">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span>
<b>by </b><i><a class="ref" href="valued_1.html#T5" title="VALUED_1:th.5">VALUED_1:5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c42">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c43">z</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c42">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c43">z</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span>
<b>by </b><i><a class="txt" href="#E11:98_8"><i><font color="Green" title="E94">A23</font></i></a>, <a class="txt" href="#E12:98_8"><i><font color="Green" title="E95">A24</font></i></a>, <a class="txt" href="#E13:98_8"><i><font color="Green" title="E96">A25</font></i></a>, <a class="txt" href="#E14:98_8"><i><font color="Green" title="E97">A26</font></i></a>, <a class="txt" href="#E15:98_8"><i><font color="Green" title="E98">A27</font></i></a>, <a class="ref" href="valued_1.html#T5" title="VALUED_1:th.5">VALUED_1:5</a></i>
;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="98_8_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:98_8_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c42">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c43">z</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c42">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c43">z</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:98_8_2"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon" title="c42">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c43">z</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c42">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c43">z</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 <b>by </b><i><a class="ref" href="complex1.html#T2" title="COMPLEX1:th.2">COMPLEX1:2</a></i>;<br/><b>hence </b><a NAME="E3:98_8_2"/>
contradiction
 <b>by </b><i><a class="txt" href="#E9:98_8"><i><font color="Green" title="E93">A22</font></i></a>, <a class="ref" href="topreal3.html#T11" title="TOPREAL3:th.11">TOPREAL3:11</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><b>hence </b><a NAME="E18:98_8"/>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c38">b</font>
 <b>by </b><i><a class="txt" href="#E4:98_8"><i><font color="Green" title="E90">A19</font></i></a>, <a class="txt" href="#E6:98_8"><i><font color="Green" title="E91">A20</font></i></a>, <a class="txt" href="#E16:98_8"><i><font color="Green" title="E99">A28</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon" title="c38">m</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> as  <a href="pscomp_1.html#V9" title="PSCOMP_1:attr.9">continuous</a> <a href="partfun3.html#V1" title="PARTFUN3:attr.1">positive-yielding</a> <a href="pscomp_1.html#NM1" title="PSCOMP_1:NM.1">RealMap</a> of <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <b>by </b><i><a class="ref" href="partfun3.html#D1" title="PARTFUN3:def.1">PARTFUN3:def 1</a></i>;<br/>
<b>set </b><font color="Maroon" title="c39">p1</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c40">p2</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K7" title="PARTFUN3:func.7">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c27">f1</font> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span>;<br/>
<a NAME="E22:98"/><i><font color="Green" title="E89">A30</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K7" title="PARTFUN3:func.7">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c27">f1</font> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="98_9"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c41">b</font> be  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c41">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K7" title="PARTFUN3:func.7">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c27">f1</font> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> implies  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c41">b</font> )</span><br/><b>assume </b><a NAME="E1:98_9"/>
<font color="Maroon" title="c41">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K7" title="PARTFUN3:func.7">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c27">f1</font> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c41">b</font></span><br/><b>then consider </b><font color="Maroon" title="c42">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:98_9"/><i><font color="Green" title="E90">A31</font></i>: 
<font color="Maroon" title="c42">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K7" title="PARTFUN3:func.7">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c27">f1</font> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E4:98_9"/><i><font color="Green" title="E91">A32</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K7" title="PARTFUN3:func.7">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c27">f1</font> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c42">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c41">b</font>
 <b>by </b><i><a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/><b>consider </b><font color="Maroon" title="c43">y</font>, <font color="Maroon" title="c44">z</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E6:98_9"/><i><font color="Green" title="E92">A33</font></i>: 
( <font color="Maroon" title="c43">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp; <font color="Maroon" title="c44">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font> &amp; <font color="Maroon" title="c42">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c43">y</font>,<font color="Maroon" title="c44">z</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> )
 <b>by </b><i><a class="txt" href="#E12:98"><i><font color="Green" title="E81">A10</font></i></a>, <a class="txt" href="#E3:98_9"><i><font color="Green" title="E90">A31</font></i></a>, <a class="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c45">y</font> = <font color="Maroon" title="c43">y</font>, <font color="Maroon" title="c46">z</font> = <font color="Maroon" title="c44">z</font> as   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <b>by </b><i><a class="txt" href="#E6:98_9"><i><font color="Green" title="E92">A33</font></i></a></i>;<br/><b>set </b><font color="Maroon" title="c47">r3</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c46">z</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span>;<br/><b>set </b><font color="Maroon" title="c48">r4</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c46">z</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span>;<br/><a NAME="E8:98_9"/><i><font color="Green" title="E93">A34</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c27">f1</font> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c45">y</font>,<font color="Maroon" title="c46">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c27">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c45">y</font>,<font color="Maroon" title="c46">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>
 <b>by </b><i><a class="txt" href="#E8:98"><i><font color="Green" title="E79">A8</font></i></a>, <a class="txt" href="#E9:98"><i><font color="Green" title="E80">A9</font></i></a>, <a class="txt" href="#E17:98"><i><font color="Green" title="E86">A15</font></i></a>, <a class="txt" href="#E6:98_9"><i><font color="Green" title="E92">A33</font></i></a></i>;<br/><a NAME="E9:98_9"/><i><font color="Green" title="E94">A35</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c45">y</font>,<font color="Maroon" title="c46">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c45">y</font>,<font color="Maroon" title="c46">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>
 <b>by </b><i><a class="txt" href="#E8:98"><i><font color="Green" title="E79">A8</font></i></a>, <a class="txt" href="#E9:98"><i><font color="Green" title="E80">A9</font></i></a>, <a class="txt" href="#E18:98"><i><font color="Green" title="E87">A16</font></i></a>, <a class="txt" href="#E6:98_9"><i><font color="Green" title="E92">A33</font></i></a></i>;<br/><a NAME="E10:98_9"/><i><font color="Green" title="E95">A36</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c45">y</font>,<font color="Maroon" title="c46">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c45">y</font>,<font color="Maroon" title="c46">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>
 <b>by </b><i><a class="txt" href="#E8:98"><i><font color="Green" title="E79">A8</font></i></a>, <a class="txt" href="#E9:98"><i><font color="Green" title="E80">A9</font></i></a>, <a class="txt" href="#E19:98"><i><font color="Green" title="E88">A17</font></i></a>, <a class="txt" href="#E6:98_9"><i><font color="Green" title="E92">A33</font></i></a></i>;<br/><a NAME="E11:98_9"/>
<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c45">y</font>,<font color="Maroon" title="c46">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c45">y</font>,<font color="Maroon" title="c46">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="jordan.html#K1" title="JORDAN:func.1">`1</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c45">y</font>,<font color="Maroon" title="c46">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="jordan.html#K2" title="JORDAN:func.2">`2</a> </span>)</span></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>
 <b>by </b><i><a class="txt" href="jordan.html#E20"><i><font color="Green" title="E15">Lm7</font></i></a>, <a class="ref" href="mcart_1.html#T23" title="MCART_1:th.23">MCART_1:23</a></i>;<br/><a NAME="E12:98_9"/><b>then </b><i><font color="Green" title="E96">A37</font></i>: 
( <font color="Maroon" title="c45">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c45">y</font>,<font color="Maroon" title="c46">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="jordan.html#K1" title="JORDAN:func.1">`1</a>  &amp; <font color="Maroon" title="c46">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c45">y</font>,<font color="Maroon" title="c46">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="jordan.html#K2" title="JORDAN:func.2">`2</a>  )
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></i>;<br/><a NAME="E13:98_9"/><i><font color="Green" title="E97">A38</font></i>: 
<span class="p1">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c45">y</font>,<font color="Maroon" title="c46">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c45">y</font>,<font color="Maroon" title="c46">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="jordan.html#K2" title="JORDAN:func.2">`2</a> </span>)</span> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span>
 <b>by </b><i><a class="ref" href="jordan.html#D1" target="_self" title="JORDAN:def.1">Def1</a></i>;<br/><a NAME="E14:98_9"/><i><font color="Green" title="E98">A39</font></i>: 
<span class="p1">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c45">y</font>,<font color="Maroon" title="c46">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c45">y</font>,<font color="Maroon" title="c46">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="jordan.html#K2" title="JORDAN:func.2">`2</a> </span>)</span> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span>
 <b>by </b><i><a class="ref" href="jordan.html#D2" target="_self" title="JORDAN:def.2">Def2</a></i>;<br/><i><font color="Green" title="E99">A40</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K7" title="PARTFUN3:func.7">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c27">f1</font> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c45">y</font>,<font color="Maroon" title="c46">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c45">y</font>,<font color="Maroon" title="c46">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c27">f1</font> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c45">y</font>,<font color="Maroon" title="c46">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span>
<b>by </b><i><a class="txt" href="#E3:98_9"><i><font color="Green" title="E90">A31</font></i></a>, <a class="txt" href="#E6:98_9"><i><font color="Green" title="E92">A33</font></i></a>, <a class="ref" href="valued_1.html#T13" title="VALUED_1:th.13">VALUED_1:13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c45">y</font>,<font color="Maroon" title="c46">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">r</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span>
<b>by </b><i><a class="txt" href="#E8:98_9"><i><font color="Green" title="E93">A34</font></i></a>, <a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c45">y</font>,<font color="Maroon" title="c46">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c45">y</font>,<font color="Maroon" title="c46">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">r</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span>
<b>by </b><i><a class="txt" href="#E3:98_9"><i><font color="Green" title="E90">A31</font></i></a>, <a class="txt" href="#E6:98_9"><i><font color="Green" title="E92">A33</font></i></a>, <a class="ref" href="valued_1.html#T1" title="VALUED_1:th.1">VALUED_1:1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p4"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c45">y</font>,<font color="Maroon" title="c46">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p4"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c45">y</font>,<font color="Maroon" title="c46">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c45">y</font>,<font color="Maroon" title="c46">z</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">r</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span>
<b>by </b><i><a class="ref" href="valued_1.html#T5" title="VALUED_1:th.5">VALUED_1:5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c46">z</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c46">z</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">r</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span>
<b>by </b><i><a class="txt" href="#E9:98_9"><i><font color="Green" title="E94">A35</font></i></a>, <a class="txt" href="#E10:98_9"><i><font color="Green" title="E95">A36</font></i></a>, <a class="txt" href="#E12:98_9"><i><font color="Green" title="E96">A37</font></i></a>, <a class="txt" href="#E13:98_9"><i><font color="Green" title="E97">A38</font></i></a>, <a class="txt" href="#E14:98_9"><i><font color="Green" title="E98">A39</font></i></a>, <a class="ref" href="valued_1.html#T5" title="VALUED_1:th.5">VALUED_1:5</a></i>
;<br/><a NAME="E16:98_9"/>
<span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c46">z</font> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <font color="Maroon" title="c7">o</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c9">r</font>
 <b>by </b><i><a class="txt" href="#E5:98"><i><font color="Green" title="E76">A5</font></i></a>, <a class="txt" href="#E6:98_9"><i><font color="Green" title="E92">A33</font></i></a>, <a class="ref" href="topreal9.html#T8" title="TOPREAL9:th.8">TOPREAL9:8</a></i>;<br/><a NAME="E17:98_9"/><b>then </b><i><font color="Green" title="E100">A41</font></i>: 
<span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c46">z</font> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <font color="Maroon" title="c7">o</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c9">r</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> 
 <b>by </b><i><a class="ref" href="square_1.html#T77" title="SQUARE_1:th.77">SQUARE_1:77</a></i>;<br/><span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c46">z</font> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <font color="Maroon" title="c7">o</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c46">z</font> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c46">z</font> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span>
<b>by </b><i><a class="ref" href="jgraph_1.html#T46" title="JGRAPH_1:th.46">JGRAPH_1:46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c46">z</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c46">z</font> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span>
<b>by </b><i><a class="ref" href="topreal3.html#T8" title="TOPREAL3:th.8">TOPREAL3:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c46">z</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c46">z</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span>
<b>by </b><i><a class="ref" href="topreal3.html#T8" title="TOPREAL3:th.8">TOPREAL3:8</a></i>
;<br/><a NAME="E19:98_9"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c46">z</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c46">z</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">r</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">r</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">r</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span>
 <b>by </b><i><a class="txt" href="#E17:98_9"><i><font color="Green" title="E100">A41</font></i></a>, <a class="ref" href="xreal_1.html#T11" title="XREAL_1:th.11">XREAL_1:11</a></i>;<br/><b>hence </b><a NAME="E20:98_9"/>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c41">b</font>
 <b>by </b><i><a class="txt" href="#E4:98_9"><i><font color="Green" title="E91">A32</font></i></a>, <a class="txt" href="#E6:98_9"><i><font color="Green" title="E92">A33</font></i></a>, <a class="txt" href="#E15:98_9"><i><font color="Green" title="E99">A40</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon" title="c41">p2</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K7" title="PARTFUN3:func.7">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c27">f1</font> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> as  <a href="pscomp_1.html#V9" title="PSCOMP_1:attr.9">continuous</a> <a href="partfun3.html#V3" title="PARTFUN3:attr.3">nonpositive-yielding</a> <a href="pscomp_1.html#NM1" title="PSCOMP_1:NM.1">RealMap</a> of <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <b>by </b><i><a class="ref" href="partfun3.html#D3" title="PARTFUN3:def.3">PARTFUN3:def 3</a></i>;<br/>
<b>set </b><font color="Maroon" title="c42">pp</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p4">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p4">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p4">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p4">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K7" title="PARTFUN3:func.7">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c38">m</font> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <font color="Maroon" title="c41">p2</font></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c43">k</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="partfun3.html#K9" title="PARTFUN3:func.9">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p0"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p1">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p5">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p0"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p1">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p0"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p1">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p5">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p0"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p1">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p2">(<span class="default"><a href="partfun3.html#K11" title="PARTFUN3:func.11">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p1">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p1">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p1">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p1">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K7" title="PARTFUN3:func.7">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c38">m</font> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <font color="Maroon" title="c41">p2</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K14" title="PARTFUN3:func.14">/</a> <font color="Maroon" title="c38">m</font>;<br/>
<b>set </b><font color="Maroon" title="c44">x3</font> = <span class="p1">(<span class="default"><a href="jordan.html#K7" title="JORDAN:func.7">Proj2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="partfun3.html#K9" title="PARTFUN3:func.9">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p1">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p1">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p4">(<span class="default"><a href="partfun3.html#K11" title="PARTFUN3:func.11">sqrt</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K7" title="PARTFUN3:func.7">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c38">m</font> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <font color="Maroon" title="c41">p2</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K14" title="PARTFUN3:func.14">/</a> <font color="Maroon" title="c38">m</font></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c45">y3</font> = <span class="p1">(<span class="default"><a href="jordan.html#K8" title="JORDAN:func.8">Proj2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="partfun3.html#K9" title="PARTFUN3:func.9">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p1">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p1">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p4">(<span class="default"><a href="partfun3.html#K11" title="PARTFUN3:func.11">sqrt</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K7" title="PARTFUN3:func.7">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c38">m</font> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <font color="Maroon" title="c41">p2</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K14" title="PARTFUN3:func.14">/</a> <font color="Maroon" title="c38">m</font></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span>;<br/>
<b>reconsider </b><font color="Maroon" title="c46">X3</font> = <span class="p1">(<span class="default"><a href="jordan.html#K7" title="JORDAN:func.7">Proj2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="partfun3.html#K9" title="PARTFUN3:func.9">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p1">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p1">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p4">(<span class="default"><a href="partfun3.html#K11" title="PARTFUN3:func.11">sqrt</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K7" title="PARTFUN3:func.7">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c38">m</font> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <font color="Maroon" title="c41">p2</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K14" title="PARTFUN3:func.14">/</a> <font color="Maroon" title="c38">m</font></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span>, <font color="Maroon" title="c47">Y3</font> = <span class="p1">(<span class="default"><a href="jordan.html#K8" title="JORDAN:func.8">Proj2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="partfun3.html#K9" title="PARTFUN3:func.9">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p1">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p1">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p4">(<span class="default"><a href="partfun3.html#K11" title="PARTFUN3:func.11">sqrt</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K7" title="PARTFUN3:func.7">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c38">m</font> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <font color="Maroon" title="c41">p2</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K14" title="PARTFUN3:func.14">/</a> <font color="Maroon" title="c38">m</font></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> as   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span>,<a href="topmetr.html#K3" title="TOPMETR:func.3">R^1</a>  <b>by </b><i><a class="ref" href="topmetr.html#T24" title="TOPMETR:th.24">TOPMETR:24</a></i>;<br/>
<b>set </b><font color="Maroon" title="c48">F</font> = <span class="p1"><a href="funct_3.html#K14" title="FUNCT_3:func.14">&lt;:</a><span class="default"><font color="Maroon" title="c46">X3</font>,<font color="Maroon" title="c47">Y3</font></span><a href="funct_3.html#K14" title="FUNCT_3:func.14">:&gt;</a></span>;<br/>
<b>set </b><font color="Maroon" title="c49">R</font> =  <a href="topreala.html#K2" title="TOPREALA:func.2">R2Homeomorphism</a> ;<br/>
<a NAME="E26:98"/><i><font color="Green" title="E90">A42</font></i>: 
for <font color="Olive" title="b1">x</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span>)</span> holds  <span class="p1">(<span class="default"><a href="jordan.html#K10" title="JORDAN:func.10">RotateCircle</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c8">p</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="topreala.html#K2" title="TOPREALA:func.2">R2Homeomorphism</a>  <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p2"><a href="funct_3.html#K14" title="FUNCT_3:func.14">&lt;:</a><span class="default"><font color="Maroon" title="c46">X3</font>,<font color="Maroon" title="c47">Y3</font></span><a href="funct_3.html#K14" title="FUNCT_3:func.14">:&gt;</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Olive" title="b1">x</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="98_10"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c50">x</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="jordan.html#K10" title="JORDAN:func.10">RotateCircle</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c8">p</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c50">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="topreala.html#K2" title="TOPREALA:func.2">R2Homeomorphism</a>  <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p2"><a href="funct_3.html#K14" title="FUNCT_3:func.14">&lt;:</a><span class="default"><font color="Maroon" title="c46">X3</font>,<font color="Maroon" title="c47">Y3</font></span><a href="funct_3.html#K14" title="FUNCT_3:func.14">:&gt;</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c50">x</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span><br/>

<b>consider </b><font color="Maroon" title="c51">y</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span><b> such that </b><br/><a NAME="E2:98_10"/><i><font color="Green" title="E91">A43</font></i>: 
( <font color="Maroon" title="c50">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c51">y</font> &amp; <span class="p1">(<span class="default"><a href="jordan.html#K10" title="JORDAN:func.10">RotateCircle</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c8">p</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c50">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="brouwer.html#K3" title="BROUWER:func.3">HC</a> <font color="Maroon" title="c51">y</font>,<font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font> )
 <b>by </b><i><a class="txt" href="#E1:98"><i><font color="Green" title="E72">A1</font></i></a>, <a class="txt" href="#E2:98"><i><font color="Green" title="E73">A2</font></i></a>, <a class="ref" href="jordan.html#D8" target="_self" title="JORDAN:def.8">Def8</a></i>;<br/>
<a NAME="E3:98_10"/><i><font color="Green" title="E92">A44</font></i>: 
<font color="Maroon" title="c50">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">p</font>
 
<b>by </b><i><a class="txt" href="#E1:98"><i><font color="Green" title="E72">A1</font></i></a>, <a class="txt" href="#E3:98"><i><font color="Green" title="E74">A3</font></i></a>, <a class="txt" href="#E9:98"><i><font color="Green" title="E80">A9</font></i></a>, <a class="ref" href="xboole_0.html#T3" title="XBOOLE_0:th.3">XBOOLE_0:3</a></i>;<br/>
<a NAME="E4:98_10"/><i><font color="Green" title="E93">A45</font></i>: 
<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span>
 
<b>by </b><i><a class="txt" href="#E4:98"><i><font color="Green" title="E75">A4</font></i></a>, <a class="txt" href="#E9:98"><i><font color="Green" title="E80">A9</font></i></a>, <a class="txt" href="#E2:98_10"><i><font color="Green" title="E91">A43</font></i></a>, <a class="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</a></i>;<br/>
<b>set </b><font color="Maroon" title="c52">r1</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c53">r2</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c54">r3</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c55">r4</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c56">l</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K7" title="SQUARE_1:func.7">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c9">r</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span></span>)</span>;<br/>
<a NAME="E5:98_10"/>
<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="jordan.html#K1" title="JORDAN:func.1">`1</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="jordan.html#K2" title="JORDAN:func.2">`2</a> </span>)</span></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>
 
<b>by </b><i><a class="txt" href="jordan.html#E20"><i><font color="Green" title="E15">Lm7</font></i></a>, <a class="ref" href="mcart_1.html#T23" title="MCART_1:th.23">MCART_1:23</a></i>;<br/>
<a NAME="E6:98_10"/><b>then </b><i><font color="Green" title="E94">A46</font></i>: 
( <font color="Maroon" title="c8">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="jordan.html#K1" title="JORDAN:func.1">`1</a>  &amp; <font color="Maroon" title="c51">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="jordan.html#K2" title="JORDAN:func.2">`2</a>  )
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></i>;<br/>
<a NAME="E7:98_10"/><i><font color="Green" title="E95">A47</font></i>: 
<a href="jordan.html#K7" title="JORDAN:func.7">Proj2_1</a>  <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="jordan.html#K2" title="JORDAN:func.2">`2</a> </span>)</span> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> 
 
<b>by </b><i><a class="ref" href="jordan.html#D5" target="_self" title="JORDAN:def.5">Def5</a></i>;<br/>
<a NAME="E8:98_10"/><i><font color="Green" title="E96">A48</font></i>: 
<a href="jordan.html#K8" title="JORDAN:func.8">Proj2_2</a>  <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="jordan.html#K2" title="JORDAN:func.2">`2</a> </span>)</span> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> 
 
<b>by </b><i><a class="ref" href="jordan.html#D6" target="_self" title="JORDAN:def.6">Def6</a></i>;<br/>
<a NAME="E9:98_10"/><i><font color="Green" title="E97">A49</font></i>: 
<a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="jordan.html#K1" title="JORDAN:func.1">`1</a> </span>)</span> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="jordan.html#K2" title="JORDAN:func.2">`2</a> </span>)</span> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="jordan.html#D3" target="_self" title="JORDAN:def.3">Def3</a></i>;<br/>
<a NAME="E10:98_10"/><i><font color="Green" title="E98">A50</font></i>: 
<a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="jordan.html#K1" title="JORDAN:func.1">`1</a> </span>)</span> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="jordan.html#K2" title="JORDAN:func.2">`2</a> </span>)</span> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="jordan.html#D4" target="_self" title="JORDAN:def.4">Def4</a></i>;<br/>
<a NAME="E11:98_10"/><i><font color="Green" title="E99">A51</font></i>: 
<span class="p1">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="jordan.html#K2" title="JORDAN:func.2">`2</a> </span>)</span> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="jordan.html#D1" target="_self" title="JORDAN:def.1">Def1</a></i>;<br/>
<a NAME="E12:98_10"/><i><font color="Green" title="E100">A52</font></i>: 
<span class="p1">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="jordan.html#K2" title="JORDAN:func.2">`2</a> </span>)</span> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="jordan.html#D2" target="_self" title="JORDAN:def.2">Def2</a></i>;<br/>
<a NAME="E13:98_10"/><i><font color="Green" title="E101">A53</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c46">X3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E14:98_10"/><i><font color="Green" title="E102">A54</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c47">Y3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E15:98_10"/><i><font color="Green" title="E103">A55</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p0"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p1">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p5">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p0"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p1">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p0"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p1">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p5">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p0"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p1">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p0"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p1">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p5">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p0"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p1">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p0"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p1">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p5">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p0"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p1">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K7" title="PARTFUN3:func.7">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c38">m</font> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <font color="Maroon" title="c41">p2</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E16:98_10"/><i><font color="Green" title="E104">A56</font></i>: 
( <font color="Maroon" title="c51">y</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span>)</span> &amp; <font color="Maroon" title="c8">p</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> )
 
<b>by </b><i><a class="txt" href="#E8:98"><i><font color="Green" title="E79">A8</font></i></a>, <a class="txt" href="#E2:98_10"><i><font color="Green" title="E91">A43</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E17:98_10"/><b>then </b><i><font color="Green" title="E105">A57</font></i>: 
<span class="p1">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>
 
<b>by </b><i><a class="txt" href="#E13:98"><i><font color="Green" title="E82">A11</font></i></a></i>;<br/>
<a NAME="E18:98_10"/><i><font color="Green" title="E106">A58</font></i>: 
<span class="p1">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>
 
<b>by </b><i><a class="txt" href="#E14:98"><i><font color="Green" title="E83">A12</font></i></a>, <a class="txt" href="#E16:98_10"><i><font color="Green" title="E104">A56</font></i></a></i>;<br/>
<a NAME="E19:98_10"/><i><font color="Green" title="E107">A59</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c27">f1</font> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c27">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>
 
<b>by </b><i><a class="txt" href="#E17:98"><i><font color="Green" title="E86">A15</font></i></a>, <a class="txt" href="#E16:98_10"><i><font color="Green" title="E104">A56</font></i></a></i>;<br/>
<a NAME="E20:98_10"/><i><font color="Green" title="E108">A60</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>
 
<b>by </b><i><a class="txt" href="#E18:98"><i><font color="Green" title="E87">A16</font></i></a>, <a class="txt" href="#E16:98_10"><i><font color="Green" title="E104">A56</font></i></a></i>;<br/>
<a NAME="E21:98_10"/><i><font color="Green" title="E109">A61</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>
 
<b>by </b><i><a class="txt" href="#E19:98"><i><font color="Green" title="E88">A17</font></i></a>, <a class="txt" href="#E16:98_10"><i><font color="Green" title="E104">A56</font></i></a></i>;<br/>
<i><font color="Green" title="E110">A62</font></i>: <font color="Maroon" title="c38">m</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span>
<b>by </b><i><a class="txt" href="#E12:98"><i><font color="Green" title="E81">A10</font></i></a>, <a class="txt" href="#E4:98_10"><i><font color="Green" title="E93">A45</font></i></a>, <a class="ref" href="valued_1.html#T1" title="VALUED_1:th.1">VALUED_1:1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span>
<b>by </b><i><a class="ref" href="valued_1.html#T5" title="VALUED_1:th.5">VALUED_1:5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span>
<b>by </b><i><a class="txt" href="#E6:98_10"><i><font color="Green" title="E94">A46</font></i></a>, <a class="txt" href="#E9:98_10"><i><font color="Green" title="E97">A49</font></i></a>, <a class="txt" href="#E10:98_10"><i><font color="Green" title="E98">A50</font></i></a>, <a class="txt" href="#E17:98_10"><i><font color="Green" title="E105">A57</font></i></a>, <a class="txt" href="#E18:98_10"><i><font color="Green" title="E106">A58</font></i></a>, <a class="ref" href="valued_1.html#T5" title="VALUED_1:th.5">VALUED_1:5</a></i>
;<br/>
<a NAME="E23:98_10"/><i><font color="Green" title="E111">A63</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="valued_1.html#T5" title="VALUED_1:th.5">VALUED_1:5</a></i>;<br/>
<a NAME="E24:98_10"/><i><font color="Green" title="E112">A64</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="valued_1.html#T5" title="VALUED_1:th.5">VALUED_1:5</a></i>;<br/>
<a NAME="E25:98_10"/><i><font color="Green" title="E113">A65</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span>
 
<b>by </b><i><a class="txt" href="#E12:98"><i><font color="Green" title="E81">A10</font></i></a>, <a class="txt" href="#E4:98_10"><i><font color="Green" title="E93">A45</font></i></a>, <a class="ref" href="valued_1.html#T1" title="VALUED_1:th.1">VALUED_1:1</a></i>;<br/>
<a NAME="E26:98_10"/><b>then </b><i><font color="Green" title="E114">A66</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p4">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p4">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p4">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p4">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> 
 
<b>by </b><i><a class="txt" href="#E6:98_10"><i><font color="Green" title="E94">A46</font></i></a>, <a class="txt" href="#E9:98_10"><i><font color="Green" title="E97">A49</font></i></a>, <a class="txt" href="#E10:98_10"><i><font color="Green" title="E98">A50</font></i></a>, <a class="txt" href="#E11:98_10"><i><font color="Green" title="E99">A51</font></i></a>, <a class="txt" href="#E12:98_10"><i><font color="Green" title="E100">A52</font></i></a>, <a class="txt" href="#E17:98_10"><i><font color="Green" title="E105">A57</font></i></a>, <a class="txt" href="#E18:98_10"><i><font color="Green" title="E106">A58</font></i></a>, <a class="txt" href="#E20:98_10"><i><font color="Green" title="E108">A60</font></i></a>, <a class="txt" href="#E21:98_10"><i><font color="Green" title="E109">A61</font></i></a>, <a class="txt" href="#E23:98_10"><i><font color="Green" title="E111">A63</font></i></a>, <a class="txt" href="#E24:98_10"><i><font color="Green" title="E112">A64</font></i></a>, <a class="ref" href="valued_1.html#T5" title="VALUED_1:th.5">VALUED_1:5</a></i>;<br/>
<i><font color="Green" title="E115">A67</font></i>: <font color="Maroon" title="c41">p2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c27">f1</font> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span>
<b>by </b><i><a class="txt" href="#E12:98"><i><font color="Green" title="E81">A10</font></i></a>, <a class="txt" href="#E22:98"><i><font color="Green" title="E89">A30</font></i></a>, <a class="txt" href="#E4:98_10"><i><font color="Green" title="E93">A45</font></i></a>, <a class="ref" href="valued_1.html#T13" title="VALUED_1:th.13">VALUED_1:13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">r</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span>
<b>by </b><i><a class="txt" href="#E19:98_10"><i><font color="Green" title="E107">A59</font></i></a>, <a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">r</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span>
<b>by </b><i><a class="txt" href="#E12:98"><i><font color="Green" title="E81">A10</font></i></a>, <a class="txt" href="#E4:98_10"><i><font color="Green" title="E93">A45</font></i></a>, <a class="ref" href="valued_1.html#T1" title="VALUED_1:th.1">VALUED_1:1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p4"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p4"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">r</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span>
<b>by </b><i><a class="ref" href="valued_1.html#T5" title="VALUED_1:th.5">VALUED_1:5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">r</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span>
<b>by </b><i><a class="txt" href="#E6:98_10"><i><font color="Green" title="E94">A46</font></i></a>, <a class="txt" href="#E11:98_10"><i><font color="Green" title="E99">A51</font></i></a>, <a class="txt" href="#E12:98_10"><i><font color="Green" title="E100">A52</font></i></a>, <a class="txt" href="#E20:98_10"><i><font color="Green" title="E108">A60</font></i></a>, <a class="txt" href="#E21:98_10"><i><font color="Green" title="E109">A61</font></i></a>, <a class="ref" href="valued_1.html#T5" title="VALUED_1:th.5">VALUED_1:5</a></i>
;<br/>
<a NAME="E28:98_10"/>
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="partfun3.html#K11" title="PARTFUN3:func.11">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p0">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p0">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p0">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p0">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K7" title="PARTFUN3:func.7">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c38">m</font> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <font color="Maroon" title="c41">p2</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<b>then </b><i><font color="Green" title="E116">A68</font></i>: <span class="p1">(<span class="default"><a href="partfun3.html#K11" title="PARTFUN3:func.11">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p0">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p0">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p0">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p0">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K7" title="PARTFUN3:func.7">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c38">m</font> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <font color="Maroon" title="c41">p2</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> = 
 <a href="square_1.html#K6" title="SQUARE_1:func.6">sqrt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p0">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p0">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p0">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p0">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K7" title="PARTFUN3:func.7">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c38">m</font> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <font color="Maroon" title="c41">p2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span>
<b>by </b><i><a class="txt" href="#E12:98"><i><font color="Green" title="E81">A10</font></i></a>, <a class="txt" href="#E4:98_10"><i><font color="Green" title="E93">A45</font></i></a>, <a class="ref" href="partfun3.html#D5" title="PARTFUN3:def.5">PARTFUN3:def 5</a></i>
<br/>.= 
 <a href="square_1.html#K6" title="SQUARE_1:func.6">sqrt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p0">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p0">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p0">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p0">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c38">m</font> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <font color="Maroon" title="c41">p2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E12:98"><i><font color="Green" title="E81">A10</font></i></a>, <a class="txt" href="#E4:98_10"><i><font color="Green" title="E93">A45</font></i></a>, <a class="txt" href="#E15:98_10"><i><font color="Green" title="E103">A55</font></i></a>, <a class="ref" href="valued_1.html#T13" title="VALUED_1:th.13">VALUED_1:13</a></i>
<br/>.= 
 <a href="square_1.html#K7" title="SQUARE_1:func.7">sqrt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c9">r</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E22:98_10"><i><font color="Green" title="E110">A62</font></i></a>, <a class="txt" href="#E26:98_10"><i><font color="Green" title="E114">A66</font></i></a>, <a class="txt" href="#E27:98_10"><i><font color="Green" title="E115">A67</font></i></a>, <a class="ref" href="valued_1.html#T5" title="VALUED_1:th.5">VALUED_1:5</a></i>
;<br/>
<a NAME="E30:98_10"/>
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="partfun3.html#K9" title="PARTFUN3:func.9">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p0">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p0">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p3">(<span class="default"><a href="partfun3.html#K11" title="PARTFUN3:func.11">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K7" title="PARTFUN3:func.7">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c38">m</font> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <font color="Maroon" title="c41">p2</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K14" title="PARTFUN3:func.14">/</a> <font color="Maroon" title="c38">m</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<b>then </b><i><font color="Green" title="E117">A69</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="partfun3.html#K9" title="PARTFUN3:func.9">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p0">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p0">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p3">(<span class="default"><a href="partfun3.html#K11" title="PARTFUN3:func.11">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K7" title="PARTFUN3:func.7">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c38">m</font> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <font color="Maroon" title="c41">p2</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K14" title="PARTFUN3:func.14">/</a> <font color="Maroon" title="c38">m</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="partfun3.html#K9" title="PARTFUN3:func.9">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p0">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p0">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p3">(<span class="default"><a href="partfun3.html#K11" title="PARTFUN3:func.11">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K7" title="PARTFUN3:func.7">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c38">m</font> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <font color="Maroon" title="c41">p2</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c38">m</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span> <a href="xcmplx_0.html#K5" title="XCMPLX_0:func.5">"</a> </span>)</span>
<b>by </b><i><a class="txt" href="#E12:98"><i><font color="Green" title="E81">A10</font></i></a>, <a class="txt" href="#E4:98_10"><i><font color="Green" title="E93">A45</font></i></a>, <a class="ref" href="rfunct_1.html#D4" title="RFUNCT_1:def.4">RFUNCT_1:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="partfun3.html#K9" title="PARTFUN3:func.9">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p0">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p0">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p3">(<span class="default"><a href="partfun3.html#K11" title="PARTFUN3:func.11">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K7" title="PARTFUN3:func.7">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c38">m</font> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <font color="Maroon" title="c41">p2</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c38">m</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_0.html#D9" title="XCMPLX_0:def.9">XCMPLX_0:def 9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="partfun3.html#K9" title="PARTFUN3:func.9">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p0">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p0">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="partfun3.html#K11" title="PARTFUN3:func.11">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K7" title="PARTFUN3:func.7">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c38">m</font> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <font color="Maroon" title="c41">p2</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E12:98"><i><font color="Green" title="E81">A10</font></i></a>, <a class="txt" href="#E4:98_10"><i><font color="Green" title="E93">A45</font></i></a>, <a class="txt" href="#E22:98_10"><i><font color="Green" title="E110">A62</font></i></a>, <a class="ref" href="valued_1.html#T1" title="VALUED_1:th.1">VALUED_1:1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K7" title="SQUARE_1:func.7">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c9">r</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E6:98_10"><i><font color="Green" title="E94">A46</font></i></a>, <a class="txt" href="#E9:98_10"><i><font color="Green" title="E97">A49</font></i></a>, <a class="txt" href="#E10:98_10"><i><font color="Green" title="E98">A50</font></i></a>, <a class="txt" href="#E11:98_10"><i><font color="Green" title="E99">A51</font></i></a>, <a class="txt" href="#E12:98_10"><i><font color="Green" title="E100">A52</font></i></a>, <a class="txt" href="#E17:98_10"><i><font color="Green" title="E105">A57</font></i></a>, <a class="txt" href="#E18:98_10"><i><font color="Green" title="E106">A58</font></i></a>, <a class="txt" href="#E20:98_10"><i><font color="Green" title="E108">A60</font></i></a>, <a class="txt" href="#E21:98_10"><i><font color="Green" title="E109">A61</font></i></a>, <a class="txt" href="#E23:98_10"><i><font color="Green" title="E111">A63</font></i></a>, <a class="txt" href="#E24:98_10"><i><font color="Green" title="E112">A64</font></i></a>, <a class="txt" href="#E25:98_10"><i><font color="Green" title="E113">A65</font></i></a>, <a class="txt" href="#E29:98_10"><i><font color="Green" title="E116">A68</font></i></a>, <a class="ref" href="valued_1.html#T8" title="VALUED_1:th.8">VALUED_1:8</a></i>
;<br/>
<i><font color="Green" title="E118">A70</font></i>: <font color="Maroon" title="c46">X3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K7" title="JORDAN:func.7">Proj2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="partfun3.html#K9" title="PARTFUN3:func.9">-</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p5">(<span class="default"><a href="partfun3.html#K11" title="PARTFUN3:func.11">sqrt</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p4">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p4">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p4">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p4">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K7" title="PARTFUN3:func.7">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c38">m</font> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <font color="Maroon" title="c41">p2</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K14" title="PARTFUN3:func.14">/</a> <font color="Maroon" title="c38">m</font></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span>
<b>by </b><i><a class="txt" href="#E12:98"><i><font color="Green" title="E81">A10</font></i></a>, <a class="txt" href="#E4:98_10"><i><font color="Green" title="E93">A45</font></i></a>, <a class="ref" href="valued_1.html#T1" title="VALUED_1:th.1">VALUED_1:1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="partfun3.html#K9" title="PARTFUN3:func.9">-</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p5">(<span class="default"><a href="partfun3.html#K11" title="PARTFUN3:func.11">sqrt</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p4">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p4">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p4">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p4">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K7" title="PARTFUN3:func.7">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c38">m</font> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <font color="Maroon" title="c41">p2</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K14" title="PARTFUN3:func.14">/</a> <font color="Maroon" title="c38">m</font></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span>
<b>by </b><i><a class="txt" href="#E15:98"><i><font color="Green" title="E84">A13</font></i></a>, <a class="txt" href="#E6:98_10"><i><font color="Green" title="E94">A46</font></i></a>, <a class="txt" href="#E7:98_10"><i><font color="Green" title="E95">A47</font></i></a>, <a class="txt" href="#E16:98_10"><i><font color="Green" title="E104">A56</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><a href="square_1.html#K7" title="SQUARE_1:func.7">sqrt</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">r</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E6:98_10"><i><font color="Green" title="E94">A46</font></i></a>, <a class="txt" href="#E9:98_10"><i><font color="Green" title="E97">A49</font></i></a>, <a class="txt" href="#E17:98_10"><i><font color="Green" title="E105">A57</font></i></a>, <a class="txt" href="#E31:98_10"><i><font color="Green" title="E117">A69</font></i></a>, <a class="ref" href="valued_1.html#T5" title="VALUED_1:th.5">VALUED_1:5</a></i>
;<br/>
<i><font color="Green" title="E119">A71</font></i>: <font color="Maroon" title="c47">Y3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan.html#K8" title="JORDAN:func.8">Proj2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="partfun3.html#K9" title="PARTFUN3:func.9">-</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p5">(<span class="default"><a href="partfun3.html#K11" title="PARTFUN3:func.11">sqrt</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p4">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p4">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p4">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p4">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K7" title="PARTFUN3:func.7">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c38">m</font> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <font color="Maroon" title="c41">p2</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K14" title="PARTFUN3:func.14">/</a> <font color="Maroon" title="c38">m</font></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span>
<b>by </b><i><a class="txt" href="#E12:98"><i><font color="Green" title="E81">A10</font></i></a>, <a class="txt" href="#E4:98_10"><i><font color="Green" title="E93">A45</font></i></a>, <a class="ref" href="valued_1.html#T1" title="VALUED_1:th.1">VALUED_1:1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="partfun3.html#K9" title="PARTFUN3:func.9">-</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p2">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p5">(<span class="default"><a href="partfun3.html#K11" title="PARTFUN3:func.11">sqrt</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p4">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p4">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K3" title="JORDAN:func.3">diffX2_1</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p4">(<span class="default"><a href="jordan.html#K5" title="JORDAN:func.5">diffX1_X2_1</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="partfun3.html#K6" title="PARTFUN3:func.6">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="jordan.html#K4" title="JORDAN:func.4">diffX2_2</a> <font color="Maroon" title="c7">o</font></span>)</span> <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p4">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p5"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p0"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p0">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K7" title="PARTFUN3:func.7">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c38">m</font> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <font color="Maroon" title="c41">p2</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun3.html#K14" title="PARTFUN3:func.14">/</a> <font color="Maroon" title="c38">m</font></span>)</span> <a href="partfun3.html#K8" title="PARTFUN3:func.8">(#)</a> <span class="p3">(<span class="default"><a href="jordan.html#K6" title="JORDAN:func.6">diffX1_X2_2</a>  <a href="pscomp_1.html#K8" title="PSCOMP_1:func.8">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span>
<b>by </b><i><a class="txt" href="#E16:98"><i><font color="Green" title="E85">A14</font></i></a>, <a class="txt" href="#E6:98_10"><i><font color="Green" title="E94">A46</font></i></a>, <a class="txt" href="#E8:98_10"><i><font color="Green" title="E96">A48</font></i></a>, <a class="txt" href="#E16:98_10"><i><font color="Green" title="E104">A56</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><a href="square_1.html#K7" title="SQUARE_1:func.7">sqrt</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">r</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E6:98_10"><i><font color="Green" title="E94">A46</font></i></a>, <a class="txt" href="#E10:98_10"><i><font color="Green" title="E98">A50</font></i></a>, <a class="txt" href="#E18:98_10"><i><font color="Green" title="E106">A58</font></i></a>, <a class="txt" href="#E31:98_10"><i><font color="Green" title="E117">A69</font></i></a>, <a class="ref" href="valued_1.html#T5" title="VALUED_1:th.5">VALUED_1:5</a></i>
;<br/>
<a NAME="E34:98_10"/>
<font color="Maroon" title="c51">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="#E2:98_10"><i><font color="Green" title="E91">A43</font></i></a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><a href="jordan.html#K10" title="JORDAN:func.10">RotateCircle</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c8">p</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c50">x</font> = 
<span class="p1"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><a href="square_1.html#K7" title="SQUARE_1:func.7">sqrt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c9">r</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><a href="square_1.html#K7" title="SQUARE_1:func.7">sqrt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">o</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c9">r</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c51">y</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span>
<b>by </b><i><a class="txt" href="#E1:98"><i><font color="Green" title="E72">A1</font></i></a>, <a class="txt" href="#E5:98"><i><font color="Green" title="E76">A5</font></i></a>, <a class="txt" href="#E6:98"><i><font color="Green" title="E77">A6</font></i></a>, <a class="txt" href="#E7:98"><i><font color="Green" title="E78">A7</font></i></a>, <a class="txt" href="#E9:98"><i><font color="Green" title="E80">A9</font></i></a>, <a class="txt" href="#E2:98_10"><i><font color="Green" title="E91">A43</font></i></a>, <a class="txt" href="#E3:98_10"><i><font color="Green" title="E92">A44</font></i></a>, <a class="ref" href="brouwer.html#T8" title="BROUWER:th.8">BROUWER:8</a></i>
<br/>.= 
<a href="topreala.html#K2" title="TOPREALA:func.2">R2Homeomorphism</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c46">X3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c47">Y3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<b>by </b><i><a class="txt" href="#E32:98_10"><i><font color="Green" title="E118">A70</font></i></a>, <a class="txt" href="#E33:98_10"><i><font color="Green" title="E119">A71</font></i></a>, <a class="ref" href="topreala.html#D2" title="TOPREALA:def.2">TOPREALA:def 2</a></i>
<br/>.= 
<a href="topreala.html#K2" title="TOPREALA:func.2">R2Homeomorphism</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2"><a href="funct_3.html#K14" title="FUNCT_3:func.14">&lt;:</a><span class="default"><font color="Maroon" title="c46">X3</font>,<font color="Maroon" title="c47">Y3</font></span><a href="funct_3.html#K14" title="FUNCT_3:func.14">:&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">y</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span>
<b>by </b><i><a class="txt" href="#E12:98"><i><font color="Green" title="E81">A10</font></i></a>, <a class="txt" href="#E4:98_10"><i><font color="Green" title="E93">A45</font></i></a>, <a class="txt" href="#E13:98_10"><i><font color="Green" title="E101">A53</font></i></a>, <a class="txt" href="#E14:98_10"><i><font color="Green" title="E102">A54</font></i></a>, <a class="ref" href="funct_3.html#T69" title="FUNCT_3:th.69">FUNCT_3:69</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="topreala.html#K2" title="TOPREALA:func.2">R2Homeomorphism</a>  <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p2"><a href="funct_3.html#K14" title="FUNCT_3:func.14">&lt;:</a><span class="default"><font color="Maroon" title="c46">X3</font>,<font color="Maroon" title="c47">Y3</font></span><a href="funct_3.html#K14" title="FUNCT_3:func.14">:&gt;</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c50">x</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>
<b>by </b><i><a class="txt" href="#E12:98"><i><font color="Green" title="E81">A10</font></i></a>, <a class="txt" href="#E2:98_10"><i><font color="Green" title="E91">A43</font></i></a>, <a class="txt" href="#E4:98_10"><i><font color="Green" title="E93">A45</font></i></a>, <a class="ref" href="funct_2.html#T21" title="FUNCT_2:th.21">FUNCT_2:21</a></i>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E27:98"/>
( <font color="Maroon" title="c46">X3</font> is <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a> &amp; <font color="Maroon" title="c47">Y3</font> is <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a> )
 
<b>by </b><i><a class="ref" href="topreal6.html#T83" title="TOPREAL6:th.83">TOPREAL6:83</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c50">F</font> = <span class="p1"><a href="funct_3.html#K14" title="FUNCT_3:func.14">&lt;:</a><span class="default"><font color="Maroon" title="c46">X3</font>,<font color="Maroon" title="c47">Y3</font></span><a href="funct_3.html#K14" title="FUNCT_3:func.14">:&gt;</a></span> as  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a> <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span>,<span class="p1"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><a href="topmetr.html#K3" title="TOPMETR:func.3">R^1</a> ,<a href="topmetr.html#K3" title="TOPMETR:func.3">R^1</a> </span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span> <b>by </b><i><a class="ref" href="yellow12.html#T41" title="YELLOW12:th.41">YELLOW12:41</a></i>;<br/>
<a NAME="E29:98"/>
for <font color="Olive" title="b1">pp</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span>)</span><br/> for <font color="Olive" title="b2">V</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="toprealb.html#K7" title="TOPREALB:func.7">Tcircle</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span>  st <span class="p1">(<span class="default"><a href="jordan.html#K10" title="JORDAN:func.10">RotateCircle</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c8">p</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">pp</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">V</font> &amp; <font color="Olive" title="b2">V</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> holds <br/> ex <font color="Olive" title="b3">W</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span>)</span> st <br/>( <font color="Olive" title="b1">pp</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b3">W</font> &amp; <font color="Olive" title="b3">W</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> &amp; <span class="p1">(<span class="default"><a href="jordan.html#K10" title="JORDAN:func.10">RotateCircle</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c8">p</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Olive" title="b3">W</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">V</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="98_11"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c51">pp</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">V</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="toprealb.html#K7" title="TOPREALB:func.7">Tcircle</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span>  st <span class="p1">(<span class="default"><a href="jordan.html#K10" title="JORDAN:func.10">RotateCircle</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c8">p</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c51">pp</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">V</font> &amp; <font color="Olive" title="b1">V</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> holds <br/> ex <font color="Olive" title="b2">W</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span>)</span> st <br/>( <font color="Maroon" title="c51">pp</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">W</font> &amp; <font color="Olive" title="b2">W</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> &amp; <span class="p1">(<span class="default"><a href="jordan.html#K10" title="JORDAN:func.10">RotateCircle</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c8">p</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Olive" title="b2">W</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">V</font> )</span><br/><b>let </b><font color="Maroon" title="c52">V</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="toprealb.html#K7" title="TOPREALB:func.7">Tcircle</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="jordan.html#K10" title="JORDAN:func.10">RotateCircle</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c8">p</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c51">pp</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c52">V</font> &amp; <font color="Maroon" title="c52">V</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> implies  ex <font color="Olive" title="b1">W</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span>)</span> st <br/>( <font color="Maroon" title="c51">pp</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">W</font> &amp; <font color="Olive" title="b1">W</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> &amp; <span class="p1">(<span class="default"><a href="jordan.html#K10" title="JORDAN:func.10">RotateCircle</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c8">p</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Olive" title="b1">W</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c52">V</font> ) )</span><br/>



<b>assume </b><b>that </b><br/><a NAME="E1:98_11"/><i><font color="Green" title="E91">A72</font></i>: 
<span class="p1">(<span class="default"><a href="jordan.html#K10" title="JORDAN:func.10">RotateCircle</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c8">p</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c51">pp</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c52">V</font>
 <b>and </b><br/><a NAME="E2:98_11"/><i><font color="Green" title="E92">A73</font></i>: 
<font color="Maroon" title="c52">V</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">W</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span>)</span> st <br/>( <font color="Maroon" title="c51">pp</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">W</font> &amp; <font color="Olive" title="b1">W</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> &amp; <span class="p1">(<span class="default"><a href="jordan.html#K10" title="JORDAN:func.10">RotateCircle</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c8">p</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Olive" title="b1">W</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c52">V</font> )</span><br/>

<b>reconsider </b><font color="Maroon" title="c53">p1</font> = <font color="Maroon" title="c51">pp</font>, <font color="Maroon" title="c54">fp</font> = <font color="Maroon" title="c8">p</font> as   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <b>by </b><i><a class="ref" href="pre_topc.html#T55" title="PRE_TOPC:th.55">PRE_TOPC:55</a></i>;<br/>
<a NAME="E4:98_11"/><i><font color="Green" title="E93">A74</font></i>: 
<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">pp</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span>
 
<b>by </b><i><a class="txt" href="#E4:98"><i><font color="Green" title="E75">A4</font></i></a>, <a class="txt" href="#E9:98"><i><font color="Green" title="E80">A9</font></i></a>, <a class="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c55">V1</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span><b> such that </b><br/><a NAME="E6:98_11"/><i><font color="Green" title="E94">A75</font></i>: 
<font color="Maroon" title="c55">V1</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>
 <b>and </b><br/><a NAME="E7:98_11"/><i><font color="Green" title="E95">A76</font></i>: 
<font color="Maroon" title="c55">V1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p2">(<span class="default"><a href="toprealb.html#K7" title="TOPREALB:func.7">Tcircle</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c52">V</font>
 <b>by </b><i><a class="txt" href="#E2:98_11"><i><font color="Green" title="E92">A73</font></i></a>, <a class="ref" href="tops_2.html#T32" title="TOPS_2:th.32">TOPS_2:32</a></i>;<br/>
<a NAME="E8:98_11"/><i><font color="Green" title="E96">A77</font></i>: 
<span class="p1">(<span class="default"><a href="jordan.html#K10" title="JORDAN:func.10">RotateCircle</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c8">p</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c51">pp</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="topreala.html#K2" title="TOPREALA:func.2">R2Homeomorphism</a>  <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c50">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c51">pp</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>
 
<b>by </b><i><a class="txt" href="#E26:98"><i><font color="Green" title="E90">A42</font></i></a></i>;<br/>
<a NAME="E9:98_11"/>
<a href="topreala.html#K2" title="TOPREALA:func.2">R2Homeomorphism</a>  <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a>  is <a href="tops_2.html#V3" title="TOPS_2:attr.3">being_homeomorphism</a>
 
<b>by </b><i><a class="ref" href="topreala.html#T56" title="TOPREALA:th.56">TOPREALA:56</a>, <a class="ref" href="tops_2.html#T70" title="TOPS_2:th.70">TOPS_2:70</a></i>;<br/>
<a NAME="E10:98_11"/><b>then </b><i><font color="Green" title="E97">A78</font></i>: 
<span class="p1">(<span class="default"><a href="topreala.html#K2" title="TOPREALA:func.2">R2Homeomorphism</a>  <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a> </span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c55">V1</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>
 
<b>by </b><i><a class="txt" href="#E6:98_11"><i><font color="Green" title="E94">A75</font></i></a>, <a class="ref" href="topgrp_1.html#T25" title="TOPGRP_1:th.25">TOPGRP_1:25</a></i>;<br/>
<a NAME="E11:98_11"/><i><font color="Green" title="E98">A79</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c50">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E12:98_11"/><i><font color="Green" title="E99">A80</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <a href="topreala.html#K2" title="TOPREALA:func.2">R2Homeomorphism</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><a href="topmetr.html#K3" title="TOPMETR:func.3">R^1</a> ,<a href="topmetr.html#K3" title="TOPMETR:func.3">R^1</a> </span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E13:98_11"/><b>then </b><i><font color="Green" title="E100">A81</font></i>: 
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c50">F</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <a href="topreala.html#K2" title="TOPREALA:func.2">R2Homeomorphism</a> 
 
;<br/>
<a NAME="E14:98_11"/><b>then </b><i><font color="Green" title="E101">A82</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="topreala.html#K2" title="TOPREALA:func.2">R2Homeomorphism</a>  <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c50">F</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c50">F</font>
 
<b>by </b><i><a class="ref" href="relat_1.html#T46" title="RELAT_1:th.46">RELAT_1:46</a></i>;<br/>
<a NAME="E15:98_11"/><i><font color="Green" title="E102">A83</font></i>: 
(  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <a href="topreala.html#K2" title="TOPREALA:func.2">R2Homeomorphism</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> &amp;  <a href="topreala.html#K2" title="TOPREALA:func.2">R2Homeomorphism</a>  is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a> )
 
<b>by </b><i><a class="ref" href="topreala.html#T56" title="TOPREALA:th.56">TOPREALA:56</a>, <a class="ref" href="tops_2.html#D5" title="TOPS_2:def.5">TOPS_2:def 5</a></i>;<br/>
<i><font color="Green" title="E103">A84</font></i>: <span class="p1">(<span class="default"><a href="topreala.html#K2" title="TOPREALA:func.2">R2Homeomorphism</a>  <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a> </span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><a href="topreala.html#K2" title="TOPREALA:func.2">R2Homeomorphism</a>  <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c50">F</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="topreala.html#K2" title="TOPREALA:func.2">R2Homeomorphism</a>  <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a> </span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <a href="topreala.html#K2" title="TOPREALA:func.2">R2Homeomorphism</a> </span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c50">F</font>
<b>by </b><i><a class="ref" href="relat_1.html#T55" title="RELAT_1:th.55">RELAT_1:55</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p2">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <a href="topreala.html#K2" title="TOPREALA:func.2">R2Homeomorphism</a> </span>)</span></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c50">F</font>
<b>by </b><i><a class="txt" href="#E15:98_11"><i><font color="Green" title="E102">A83</font></i></a>, <a class="ref" href="tops_2.html#T65" title="TOPS_2:th.65">TOPS_2:65</a></i>
;<br/>
<a NAME="E17:98_11"/>
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p2">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <a href="topreala.html#K2" title="TOPREALA:func.2">R2Homeomorphism</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <a href="topreala.html#K2" title="TOPREALA:func.2">R2Homeomorphism</a> 
 
<b>by </b><i><a class="ref" href="relat_1.html#T71" title="RELAT_1:th.71">RELAT_1:71</a></i>;<br/>
<a NAME="E18:98_11"/><b>then </b><i><font color="Green" title="E104">A85</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p3">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <a href="topreala.html#K2" title="TOPREALA:func.2">R2Homeomorphism</a> </span>)</span></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c50">F</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c50">F</font>
 
<b>by </b><i><a class="txt" href="#E13:98_11"><i><font color="Green" title="E100">A81</font></i></a>, <a class="ref" href="relat_1.html#T46" title="RELAT_1:th.46">RELAT_1:46</a></i>;<br/>
<a NAME="E19:98_11"/>
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c50">F</font> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p3">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <a href="topreala.html#K2" title="TOPREALA:func.2">R2Homeomorphism</a> </span>)</span></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c50">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c50">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="98_11_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c56">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c56">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c50">F</font> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p3">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <a href="topreala.html#K2" title="TOPREALA:func.2">R2Homeomorphism</a> </span>)</span></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c50">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c56">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c50">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c56">x</font> )</span><br/>

<b>assume </b><a NAME="E1:98_11_2"/><i><font color="Green" title="E105">A86</font></i>: 
<font color="Maroon" title="c56">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c50">F</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p3">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <a href="topreala.html#K2" title="TOPREALA:func.2">R2Homeomorphism</a> </span>)</span></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c50">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c56">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c50">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c56">x</font></span><br/>

<a NAME="E2:98_11_2"/><i><font color="Green" title="E106">A87</font></i>: 
<font color="Maroon" title="c50">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c56">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c50">F</font>
 
<b>by </b><i><a class="txt" href="#E1:98_11_2"><i><font color="Green" title="E105">A86</font></i></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p3">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <a href="topreala.html#K2" title="TOPREALA:func.2">R2Homeomorphism</a> </span>)</span></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c50">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c56">x</font> = 
<span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p2">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <a href="topreala.html#K2" title="TOPREALA:func.2">R2Homeomorphism</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c50">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c56">x</font></span>)</span>
<b>by </b><i><a class="txt" href="#E1:98_11_2"><i><font color="Green" title="E105">A86</font></i></a>, <a class="ref" href="funct_1.html#T23" title="FUNCT_1:th.23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon" title="c50">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c56">x</font>
<b>by </b><i><a class="txt" href="#E12:98_11"><i><font color="Green" title="E99">A80</font></i></a>, <a class="txt" href="#E2:98_11_2"><i><font color="Green" title="E106">A87</font></i></a>, <a class="ref" href="funct_1.html#T35" title="FUNCT_1:th.35">FUNCT_1:35</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E20:98_11"/><b>then </b><i><font color="Green" title="E105">A88</font></i>: 
<span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p2">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <a href="topreala.html#K2" title="TOPREALA:func.2">R2Homeomorphism</a> </span>)</span></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c50">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c50">F</font>
 
<b>by </b><i><a class="txt" href="#E18:98_11"><i><font color="Green" title="E104">A85</font></i></a>, <a class="ref" href="funct_1.html#T9" title="FUNCT_1:th.9">FUNCT_1:9</a></i>;<br/>
<a NAME="E21:98_11"/>
<span class="p1">(<span class="default"><a href="topreala.html#K2" title="TOPREALA:func.2">R2Homeomorphism</a>  <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c50">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c54">fp</font>,<font color="Maroon" title="c53">p1</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c55">V1</font>
 
<b>by </b><i><a class="txt" href="#E1:98_11"><i><font color="Green" title="E91">A72</font></i></a>, <a class="txt" href="#E7:98_11"><i><font color="Green" title="E95">A76</font></i></a>, <a class="txt" href="#E8:98_11"><i><font color="Green" title="E96">A77</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E22:98_11"/><b>then </b>
<span class="p1">(<span class="default"><a href="topreala.html#K2" title="TOPREALA:func.2">R2Homeomorphism</a>  <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="topreala.html#K2" title="TOPREALA:func.2">R2Homeomorphism</a>  <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c50">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c54">fp</font>,<font color="Maroon" title="c53">p1</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="topreala.html#K2" title="TOPREALA:func.2">R2Homeomorphism</a>  <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a> </span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c55">V1</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#T43" title="FUNCT_2:th.43">FUNCT_2:43</a></i>;<br/>
<a NAME="E23:98_11"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="topreala.html#K2" title="TOPREALA:func.2">R2Homeomorphism</a>  <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a> </span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p2">(<span class="default"><a href="topreala.html#K2" title="TOPREALA:func.2">R2Homeomorphism</a>  <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c50">F</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c54">fp</font>,<font color="Maroon" title="c53">p1</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="topreala.html#K2" title="TOPREALA:func.2">R2Homeomorphism</a>  <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a> </span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c55">V1</font>
 
<b>by </b><i><a class="txt" href="#E12:98"><i><font color="Green" title="E81">A10</font></i></a>, <a class="txt" href="#E4:98_11"><i><font color="Green" title="E93">A74</font></i></a>, <a class="txt" href="#E11:98_11"><i><font color="Green" title="E98">A79</font></i></a>, <a class="txt" href="#E14:98_11"><i><font color="Green" title="E101">A82</font></i></a>, <a class="ref" href="funct_1.html#T23" title="FUNCT_1:th.23">FUNCT_1:23</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c56">W</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><span class="p2"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>,<span class="p3">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span><b> such that </b><br/><a NAME="E25:98_11"/><i><font color="Green" title="E106">A89</font></i>: 
<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c54">fp</font>,<font color="Maroon" title="c53">p1</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c56">W</font>
 <b>and </b><br/><a NAME="E26:98_11"/><i><font color="Green" title="E107">A90</font></i>: 
<font color="Maroon" title="c56">W</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>
 <b>and </b><br/><a NAME="E27:98_11"/><i><font color="Green" title="E108">A91</font></i>: 
<font color="Maroon" title="c50">F</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c56">W</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreala.html#K2" title="TOPREALA:func.2">R2Homeomorphism</a>  <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a> </span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c55">V1</font>
 <b>by </b><i><a class="txt" href="#E12:98"><i><font color="Green" title="E81">A10</font></i></a>, <a class="txt" href="#E4:98_11"><i><font color="Green" title="E93">A74</font></i></a>, <a class="txt" href="#E10:98_11"><i><font color="Green" title="E97">A78</font></i></a>, <a class="txt" href="#E16:98_11"><i><font color="Green" title="E103">A84</font></i></a>, <a class="txt" href="#E20:98_11"><i><font color="Green" title="E105">A88</font></i></a>, <a class="ref" href="jgraph_2.html#T20" title="JGRAPH_2:th.20">JGRAPH_2:20</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c57">WW</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span><b> such that </b><br/><a NAME="E29:98_11"/><i><font color="Green" title="E109">A92</font></i>: 
<font color="Maroon" title="c57">WW</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>
 <b>and </b><br/><a NAME="E30:98_11"/><i><font color="Green" title="E110">A93</font></i>: 
<font color="Maroon" title="c57">WW</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><span class="p4">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>,<span class="p4">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c56">W</font>
 <b>by </b><i><a class="txt" href="#E26:98_11"><i><font color="Green" title="E107">A90</font></i></a>, <a class="ref" href="tops_2.html#T32" title="TOPS_2:th.32">TOPS_2:32</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c58">SF</font> being   <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <span class="p1"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span><b> such that </b><br/><a NAME="E32:98_11"/><i><font color="Green" title="E111">A94</font></i>: 
<font color="Maroon" title="c57">WW</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Maroon" title="c58">SF</font>
 <b>and </b><br/><a NAME="E33:98_11"/><i><font color="Green" title="E112">A95</font></i>: 
for <font color="Olive" title="b1">e</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c58">SF</font> holds <br/> ex <font color="Olive" title="b2">X1</font>, <font color="Olive" title="b3">Y1</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> st <br/>( <font color="Olive" title="b1">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><font color="Olive" title="b2">X1</font>,<font color="Olive" title="b3">Y1</font></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span> &amp; <font color="Olive" title="b2">X1</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> &amp; <font color="Olive" title="b3">Y1</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> )
 <b>by </b><i><a class="txt" href="#E29:98_11"><i><font color="Green" title="E109">A92</font></i></a>, <a class="ref" href="borsuk_1.html#T45" title="BORSUK_1:th.45">BORSUK_1:45</a></i>;<br/>
<a NAME="E34:98_11"/>
<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c54">fp</font>,<font color="Maroon" title="c53">p1</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c57">WW</font>
 
<b>by </b><i><a class="txt" href="#E25:98_11"><i><font color="Green" title="E106">A89</font></i></a>, <a class="txt" href="#E30:98_11"><i><font color="Green" title="E110">A93</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c59">Z</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E36:98_11"/><i><font color="Green" title="E113">A96</font></i>: 
<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c54">fp</font>,<font color="Maroon" title="c53">p1</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c59">Z</font>
 <b>and </b><br/><a NAME="E37:98_11"/><i><font color="Green" title="E114">A97</font></i>: 
<font color="Maroon" title="c59">Z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c58">SF</font>
 <b>by </b><i><a class="txt" href="#E32:98_11"><i><font color="Green" title="E111">A94</font></i></a>, <a class="ref" href="tarski.html#D4" title="TARSKI:def.4">TARSKI:def 4</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c60">X1</font>, <font color="Maroon" title="c61">Y1</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span><b> such that </b><br/><a NAME="E39:98_11"/><i><font color="Green" title="E115">A98</font></i>: 
<font color="Maroon" title="c59">Z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><font color="Maroon" title="c60">X1</font>,<font color="Maroon" title="c61">Y1</font></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span>
 <b>and </b><br/><a NAME="E40:98_11"/>
<font color="Maroon" title="c60">X1</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>
 <b>and </b><br/><a NAME="E41:98_11"/><i><font color="Green" title="E116">A99</font></i>: 
<font color="Maroon" title="c61">Y1</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>
 <b>by </b><i><a class="txt" href="#E33:98_11"><i><font color="Green" title="E112">A95</font></i></a>, <a class="txt" href="#E37:98_11"><i><font color="Green" title="E114">A97</font></i></a></i>;<br/>
<b>set </b><font color="Maroon" title="c62">ZZ</font> = <font color="Maroon" title="c59">Z</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><span class="p4">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>,<span class="p4">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span>;<br/>
<b>reconsider </b><font color="Maroon" title="c63">XX</font> = <font color="Maroon" title="c61">Y1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p3">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span>)</span></span>)</span> as  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span>)</span> <b>by </b><i><a class="txt" href="#E41:98_11"><i><font color="Green" title="E116">A99</font></i></a>, <a class="ref" href="tops_2.html#T32" title="TOPS_2:th.32">TOPS_2:32</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c63">XX</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c51">pp</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c63">XX</font> &amp; <font color="Maroon" title="c63">XX</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> &amp; <span class="p1">(<span class="default"><a href="jordan.html#K10" title="JORDAN:func.10">RotateCircle</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c8">p</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c63">XX</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c52">V</font> )</span><br/>

<a NAME="E43:98_11"/>
<font color="Maroon" title="c51">pp</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c61">Y1</font>
 
<b>by </b><i><a class="txt" href="#E36:98_11"><i><font color="Green" title="E113">A96</font></i></a>, <a class="txt" href="#E39:98_11"><i><font color="Green" title="E115">A98</font></i></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/>
<b>hence </b><a NAME="E44:98_11"/>
<font color="Maroon" title="c51">pp</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c63">XX</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c63">XX</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> &amp; <span class="p1">(<span class="default"><a href="jordan.html#K10" title="JORDAN:func.10">RotateCircle</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c8">p</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c63">XX</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c52">V</font> )</span><br/>

<b>thus </b><a NAME="E45:98_11"/>
<font color="Maroon" title="c63">XX</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="jordan.html#K10" title="JORDAN:func.10">RotateCircle</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c8">p</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c63">XX</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c52">V</font></span><br/>

<b>let </b><font color="Maroon" title="c64">b</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c64">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="jordan.html#K10" title="JORDAN:func.10">RotateCircle</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c8">p</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c63">XX</font> or <font color="Maroon" title="c64">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c52">V</font> )</span><br/>

<b>assume </b><a NAME="E46:98_11"/>
<font color="Maroon" title="c64">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="jordan.html#K10" title="JORDAN:func.10">RotateCircle</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c8">p</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c63">XX</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c64">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c52">V</font></span><br/>

<b>then consider </b><font color="Maroon" title="c65">a</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span>)</span><b> such that </b><br/><a NAME="E48:98_11"/><i><font color="Green" title="E117">A100</font></i>: 
<font color="Maroon" title="c65">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c63">XX</font>
 <b>and </b><br/><a NAME="E49:98_11"/><i><font color="Green" title="E118">A101</font></i>: 
<font color="Maroon" title="c64">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="jordan.html#K10" title="JORDAN:func.10">RotateCircle</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c8">p</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c65">a</font>
 <b>by </b><i><a class="txt" href="#E2:98"><i><font color="Green" title="E73">A2</font></i></a>, <a class="ref" href="funct_2.html#T116" title="FUNCT_2:th.116">FUNCT_2:116</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c66">a1</font> = <font color="Maroon" title="c65">a</font>, <font color="Maroon" title="c67">fa</font> = <font color="Maroon" title="c54">fp</font> as   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <b>by </b><i><a class="ref" href="pre_topc.html#T55" title="PRE_TOPC:th.55">PRE_TOPC:55</a></i>;<br/>
<a NAME="E51:98_11"/><i><font color="Green" title="E119">A102</font></i>: 
<font color="Maroon" title="c65">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c61">Y1</font>
 
<b>by </b><i><a class="txt" href="#E48:98_11"><i><font color="Green" title="E117">A100</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E52:98_11"/><i><font color="Green" title="E120">A103</font></i>: 
<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">p</font>,<font color="Maroon" title="c65">a</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span>
 
<b>by </b><i><a class="txt" href="#E4:98"><i><font color="Green" title="E75">A4</font></i></a>, <a class="txt" href="#E9:98"><i><font color="Green" title="E80">A9</font></i></a>, <a class="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</a></i>;<br/>
<a NAME="E53:98_11"/>
<font color="Maroon" title="c67">fa</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c60">X1</font>
 
<b>by </b><i><a class="txt" href="#E36:98_11"><i><font color="Green" title="E113">A96</font></i></a>, <a class="txt" href="#E39:98_11"><i><font color="Green" title="E115">A98</font></i></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/>
<a NAME="E54:98_11"/><b>then </b>
<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c67">fa</font>,<font color="Maroon" title="c65">a</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c59">Z</font>
 
<b>by </b><i><a class="txt" href="#E39:98_11"><i><font color="Green" title="E115">A98</font></i></a>, <a class="txt" href="#E51:98_11"><i><font color="Green" title="E119">A102</font></i></a>, <a class="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</a></i>;<br/>
<a NAME="E55:98_11"/><b>then </b>
<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c67">fa</font>,<font color="Maroon" title="c65">a</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c59">Z</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><span class="p4">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>,<span class="p4">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="#E12:98"><i><font color="Green" title="E81">A10</font></i></a>, <a class="txt" href="#E52:98_11"><i><font color="Green" title="E120">A103</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E56:98_11"/><b>then </b><i><font color="Green" title="E121">A104</font></i>: 
<font color="Maroon" title="c50">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c67">fa</font>,<font color="Maroon" title="c66">a1</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c50">F</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <span class="p1">(<span class="default"><font color="Maroon" title="c59">Z</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p3">(<span class="default"><span class="p4"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><span class="p5">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>,<span class="p5">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#T43" title="FUNCT_2:th.43">FUNCT_2:43</a></i>;<br/>
<a NAME="E57:98_11"/><i><font color="Green" title="E122">A105</font></i>: 
<a href="topreala.html#K2" title="TOPREALA:func.2">R2Homeomorphism</a>  <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="topreala.html#K2" title="TOPREALA:func.2">R2Homeomorphism</a>  <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a> 
 
<b>by </b><i><a class="txt" href="#E15:98_11"><i><font color="Green" title="E102">A83</font></i></a>, <a class="ref" href="tops_2.html#D4" title="TOPS_2:def.4">TOPS_2:def 4</a></i>;<br/>
<a NAME="E58:98_11"/><i><font color="Green" title="E123">A106</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="topreala.html#K2" title="TOPREALA:func.2">R2Homeomorphism</a>  <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>
 
<b>by </b><i><a class="txt" href="#E15:98_11"><i><font color="Green" title="E102">A83</font></i></a>, <a class="ref" href="tops_2.html#T62" title="TOPS_2:th.62">TOPS_2:62</a></i>;<br/>
<a NAME="E59:98_11"/><i><font color="Green" title="E124">A107</font></i>: 
<span class="p1">(<span class="default"><a href="jordan.html#K10" title="JORDAN:func.10">RotateCircle</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c8">p</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c66">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="toprealb.html#K7" title="TOPREALB:func.7">Tcircle</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E2:98"><i><font color="Green" title="E73">A2</font></i></a>, <a class="ref" href="funct_2.html#T7" title="FUNCT_2:th.7">FUNCT_2:7</a></i>;<br/>
<a NAME="E60:98_11"/>
<font color="Maroon" title="c59">Z</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c57">WW</font>
 
<b>by </b><i><a class="txt" href="#E32:98_11"><i><font color="Green" title="E111">A94</font></i></a>, <a class="txt" href="#E37:98_11"><i><font color="Green" title="E114">A97</font></i></a>, <a class="ref" href="zfmisc_1.html#T92" title="ZFMISC_1:th.92">ZFMISC_1:92</a></i>;<br/>
<a NAME="E61:98_11"/><b>then </b>
<font color="Maroon" title="c59">Z</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><span class="p4">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>,<span class="p4">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c57">WW</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p2">(<span class="default"><span class="p3"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><span class="p4">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>,<span class="p4">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p3"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p4">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T27" title="XBOOLE_1:th.27">XBOOLE_1:27</a></i>;<br/>
<a NAME="E62:98_11"/><b>then </b>
<font color="Maroon" title="c50">F</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <span class="p1">(<span class="default"><font color="Maroon" title="c59">Z</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p3">(<span class="default"><span class="p4"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><span class="p5">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>,<span class="p5">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p4"><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">[:</a><span class="default"><span class="p5"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p5">(<span class="default"><a href="topreal9.html#K3" title="TOPREAL9:func.3">Sphere</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font></span>)</span></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c50">F</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c56">W</font>
 
<b>by </b><i><a class="txt" href="#E30:98_11"><i><font color="Green" title="E110">A93</font></i></a>, <a class="ref" href="relat_1.html#T156" title="RELAT_1:th.156">RELAT_1:156</a></i>;<br/>
<a NAME="E63:98_11"/><b>then </b>
<font color="Maroon" title="c50">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c67">fa</font>,<font color="Maroon" title="c66">a1</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c50">F</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c56">W</font>
 
<b>by </b><i><a class="txt" href="#E56:98_11"><i><font color="Green" title="E121">A104</font></i></a></i>;<br/>
<a NAME="E64:98_11"/><b>then </b>
<a href="topreala.html#K2" title="TOPREALA:func.2">R2Homeomorphism</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c50">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c67">fa</font>,<font color="Maroon" title="c66">a1</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="topreala.html#K2" title="TOPREALA:func.2">R2Homeomorphism</a>  <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="topreala.html#K2" title="TOPREALA:func.2">R2Homeomorphism</a>  <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a> </span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c55">V1</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E27:98_11"><i><font color="Green" title="E108">A91</font></i></a>, <a class="ref" href="funct_2.html#T43" title="FUNCT_2:th.43">FUNCT_2:43</a></i>;<br/>
<a NAME="E65:98_11"/><b>then </b>
<span class="p1">(<span class="default"><a href="topreala.html#K2" title="TOPREALA:func.2">R2Homeomorphism</a>  <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c50">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c67">fa</font>,<font color="Maroon" title="c66">a1</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="topreala.html#K2" title="TOPREALA:func.2">R2Homeomorphism</a>  <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="topreala.html#K2" title="TOPREALA:func.2">R2Homeomorphism</a>  <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a> </span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c55">V1</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E12:98"><i><font color="Green" title="E81">A10</font></i></a>, <a class="txt" href="#E52:98_11"><i><font color="Green" title="E120">A103</font></i></a>, <a class="ref" href="funct_2.html#T21" title="FUNCT_2:th.21">FUNCT_2:21</a></i>;<br/>
<a NAME="E66:98_11"/><b>then </b>
<span class="p1">(<span class="default"><a href="topreala.html#K2" title="TOPREALA:func.2">R2Homeomorphism</a>  <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c50">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c67">fa</font>,<font color="Maroon" title="c66">a1</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c55">V1</font>
 
<b>by </b><i><a class="txt" href="#E15:98_11"><i><font color="Green" title="E102">A83</font></i></a>, <a class="txt" href="#E57:98_11"><i><font color="Green" title="E122">A105</font></i></a>, <a class="txt" href="#E58:98_11"><i><font color="Green" title="E123">A106</font></i></a>, <a class="ref" href="partfun3.html#T1" title="PARTFUN3:th.1">PARTFUN3:1</a></i>;<br/>
<a NAME="E67:98_11"/><b>then </b>
<span class="p1">(<span class="default"><a href="jordan.html#K10" title="JORDAN:func.10">RotateCircle</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c8">p</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c65">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c55">V1</font>
 
<b>by </b><i><a class="txt" href="#E26:98"><i><font color="Green" title="E90">A42</font></i></a></i>;<br/>
<b>hence </b><a NAME="E68:98_11"/>
<font color="Maroon" title="c64">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c52">V</font>
 <b>by </b><i><a class="txt" href="#E7:98_11"><i><font color="Green" title="E95">A76</font></i></a>, <a class="txt" href="#E49:98_11"><i><font color="Green" title="E118">A101</font></i></a>, <a class="txt" href="#E59:98_11"><i><font color="Green" title="E124">A107</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E30:98"/>
 <a href="jordan.html#K10" title="JORDAN:func.10">RotateCircle</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c8">p</font> is <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>
 <b>by </b><i><a class="txt" href="#E2:98"><i><font color="Green" title="E73">A2</font></i></a>, <a class="ref" href="jgraph_2.html#T20" title="JGRAPH_2:th.20">JGRAPH_2:20</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
