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

<b>let </b><font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c2">b</font>, <font color="Maroon" title="c3">c</font>, <font color="Maroon" title="c4">d</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> ;<br/>

<b>assume </b><a NAME="E1:44"/><i><font color="Green" title="E35">A1</font></i>: 
<font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c2">b</font>
 ;<br/>

<b>assume </b><a NAME="E2:44"/><i><font color="Green" title="E36">A2</font></i>: 
<font color="Maroon" title="c3">c</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">d</font>
 ;<br/>

<b>let </b><font color="Maroon" title="c5">x</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> ;<br/>

<b>assume </b><a NAME="E3:44"/><i><font color="Green" title="E37">A3</font></i>: 
<font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c5">x</font>
 ;<br/>

<b>assume </b><a NAME="E4:44"/><i><font color="Green" title="E38">A4</font></i>: 
<font color="Maroon" title="c5">x</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">b</font>
 ;<br/>

<b>set </b><font color="Maroon" title="c6">f</font> =  <a href="borsuk_6.html#K1" title="BORSUK_6:func.1">L[01]</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c4">d</font>;<br/>
<b>set </b><font color="Maroon" title="c7">F</font> =  <a href="treal_1.html#K3" title="TREAL_1:func.3">L[01]</a> <span class="p1">(<span class="default"><a href="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c4">d</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c4">d</font> <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a> </span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c8">G</font> =  <a href="treal_1.html#K4" title="TREAL_1:func.4">P[01]</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<span class="p1">(<span class="default"><a href="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> 0,1</span>)</span>,<span class="p1">(<span class="default">0,1 <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a> </span>)</span>;<br/>
<a NAME="E5:44"/><i><font color="Green" title="E39">A5</font></i>: 
(  <a href="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c4">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">c</font> &amp; <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c4">d</font> <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">d</font> )
 
<b>by </b><i><a class="txt" href="borsuk_6.html#E2:44"><i><font color="Green" title="E36">A2</font></i></a>, <a class="ref" href="treal_1.html#D1" title="TREAL_1:def.1">TREAL_1:def 1</a>, <a class="ref" href="treal_1.html#D2" title="TREAL_1:def.2">TREAL_1:def 2</a></i>;<br/>
<a NAME="E6:44"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>
 
<b>by </b><i><a class="txt" href="borsuk_6.html#E3:44"><i><font color="Green" title="E37">A3</font></i></a>, <a class="txt" href="borsuk_6.html#E4:44"><i><font color="Green" title="E38">A4</font></i></a>, <a class="ref" href="rcomp_1.html#T48" title="RCOMP_1:th.48">RCOMP_1:48</a></i>;<br/>
<a NAME="E7:44"/><b>then </b><i><font color="Green" title="E40">A6</font></i>: 
<font color="Maroon" title="c5">x</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="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font></span>)</span>
 
<b>by </b><i><a class="txt" href="borsuk_6.html#E1:44"><i><font color="Green" title="E35">A1</font></i></a>, <a class="ref" href="topmetr.html#T25" title="TOPMETR:th.25">TOPMETR:25</a></i>;<br/>
<a NAME="E8:44"/><b>then </b><i><font color="Green" title="E41">A7</font></i>: 
<font color="Maroon" title="c5">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> <span class="p1">(<span class="default"><a href="treal_1.html#K4" title="TREAL_1:func.4">P[01]</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<span class="p2">(<span class="default"><a href="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> 0,1</span>)</span>,<span class="p2">(<span class="default">0,1 <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a> </span>)</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="E9:44"/><i><font color="Green" title="E42">A8</font></i>: 
( 0 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> 0,1 &amp; 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0,1 <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a>  )
 
<b>by </b><i><a class="ref" href="treal_1.html#D1" title="TREAL_1:def.1">TREAL_1:def 1</a>, <a class="ref" href="treal_1.html#D2" title="TREAL_1:def.2">TREAL_1:def 2</a></i>;<br/>
<b>set </b><font color="Maroon" title="c9">X</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">a</font></span>)</span>;<br/>
<a NAME="E10:44"/><i><font color="Green" title="E43">A9</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">a</font></span>)</span> <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="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> 0,1</span>)</span>
 
<b>by </b><i><a class="txt" href="borsuk_6.html#E3:44"><i><font color="Green" title="E37">A3</font></i></a>, <a class="txt" href="borsuk_6.html#E4:44"><i><font color="Green" title="E38">A4</font></i></a>, <a class="ref" href="borsuk_6.html#T5" target="_self" title="BORSUK_6:th.5">Th5</a></i>;<br/>
<span class="p1">(<span class="default"><a href="borsuk_6.html#K1" title="BORSUK_6:func.1">L[01]</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c4">d</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font> = 
<span class="p1">(<span class="default"><a href="treal_1.html#K3" title="TREAL_1:func.3">L[01]</a> <span class="p2">(<span class="default"><a href="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c4">d</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c4">d</font> <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a> </span>)</span></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="treal_1.html#K4" title="TREAL_1:func.4">P[01]</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<span class="p3">(<span class="default"><a href="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> 0,1</span>)</span>,<span class="p3">(<span class="default">0,1 <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font></span>)</span>
<b>by </b><i><a class="txt" href="borsuk_6.html#E8:44"><i><font color="Green" title="E41">A7</font></i></a>, <a class="ref" href="funct_1.html#T23" title="FUNCT_1:th.23">FUNCT_1:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="treal_1.html#K3" title="TREAL_1:func.3">L[01]</a> <span class="p2">(<span class="default"><a href="treal_1.html#K1" title="TREAL_1:func.1">(#)</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c4">d</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c4">d</font> <a href="treal_1.html#K2" title="TREAL_1:func.2">(#)</a> </span>)</span></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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c5">x</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> 0</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">a</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="borsuk_6.html#E1:44"><i><font color="Green" title="E35">A1</font></i></a>, <a class="txt" href="borsuk_6.html#E7:44"><i><font color="Green" title="E40">A6</font></i></a>, <a class="txt" href="borsuk_6.html#E9:44"><i><font color="Green" title="E42">A8</font></i></a>, <a class="ref" href="treal_1.html#D4" title="TREAL_1:def.4">TREAL_1:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">a</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c3">c</font></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"><font color="Maroon" title="c5">x</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c4">d</font></span>)</span>
<b>by </b><i><a class="txt" href="borsuk_6.html#E2:44"><i><font color="Green" title="E36">A2</font></i></a>, <a class="txt" href="borsuk_6.html#E5:44"><i><font color="Green" title="E39">A5</font></i></a>, <a class="txt" href="borsuk_6.html#E10:44"><i><font color="Green" title="E43">A9</font></i></a>, <a class="ref" href="treal_1.html#D3" title="TREAL_1:def.3">TREAL_1:def 3</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="c4">d</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">c</font>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T236" title="XCMPLX_1:th.236">XCMPLX_1:236</a></i>
;<br/>
<b>hence </b><a NAME="E12:44"/>
<span class="p1">(<span class="default"><a href="borsuk_6.html#K1" title="BORSUK_6:func.1">L[01]</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c4">d</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font> <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"><font color="Maroon" title="c4">d</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">c</font>
 ;<br/>


</div>
