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

<a NAME="E1:28_1_1"/>
for <font color="Olive" title="b1">p</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c6">S</font><br/> for <font color="Olive" title="b2">V</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c8">Y</font>  st <span class="p1">(<span class="default"><a href="topalg_5.html#K3" title="TOPALG_5:func.3">Prj1</a> <font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c9">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">p</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 <font color="Maroon" title="c6">S</font> st <br/>( <font color="Olive" title="b1">p</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="topalg_5.html#K3" title="TOPALG_5:func.3">Prj1</a> <font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c9">H</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="28_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c11">p</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c6">S</font>; <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 <font color="Maroon" title="c8">Y</font>  st <span class="p1">(<span class="default"><a href="topalg_5.html#K3" title="TOPALG_5:func.3">Prj1</a> <font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c9">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">p</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 <font color="Maroon" title="c6">S</font> st <br/>( <font color="Maroon" title="c11">p</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="topalg_5.html#K3" title="TOPALG_5:func.3">Prj1</a> <font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c9">H</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="c12">V</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c8">Y</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"><a href="topalg_5.html#K3" title="TOPALG_5:func.3">Prj1</a> <font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c9">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">V</font> &amp; <font color="Maroon" title="c12">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 <font color="Maroon" title="c6">S</font> st <br/>( <font color="Maroon" title="c11">p</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="topalg_5.html#K3" title="TOPALG_5:func.3">Prj1</a> <font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c9">H</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="c12">V</font> ) )</span><br/>



<b>assume </b><b>that </b><br/><a NAME="E1:28_1_1_1"/><i><font color="Green" title="E28">A1</font></i>: 
<span class="p1">(<span class="default"><a href="topalg_5.html#K3" title="TOPALG_5:func.3">Prj1</a> <font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c9">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">V</font>
 <b>and </b><br/><a NAME="E2:28_1_1_1"/><i><font color="Green" title="E29">A2</font></i>: 
<font color="Maroon" title="c12">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 <font color="Maroon" title="c6">S</font> st <br/>( <font color="Maroon" title="c11">p</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="topalg_5.html#K3" title="TOPALG_5:func.3">Prj1</a> <font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c9">H</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="c12">V</font> )</span><br/>

<a NAME="E3:28_1_1_1"/>
<span class="p1">(<span class="default"><a href="topalg_5.html#K3" title="TOPALG_5:func.3">Prj1</a> <font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c9">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">H</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c11">p</font>,<font color="Maroon" title="c10">t</font>
 
<b>by </b><i><a class="ref" href="topalg_5.html#D2" target="_self" title="TOPALG_5:def.2">Def2</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c13">W</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"><font color="Maroon" title="c6">S</font>,<font color="Maroon" title="c7">T</font></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span><b> such that </b><br/><a NAME="E5:28_1_1_1"/><i><font color="Green" title="E30">A3</font></i>: 
<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c11">p</font>,<font color="Maroon" title="c10">t</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="c13">W</font>
 <b>and </b><br/><a NAME="E6:28_1_1_1"/><i><font color="Green" title="E31">A4</font></i>: 
<font color="Maroon" title="c13">W</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>
 <b>and </b><br/><a NAME="E7:28_1_1_1"/><i><font color="Green" title="E32">A5</font></i>: 
<font color="Maroon" title="c9">H</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c13">W</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c12">V</font>
 <b>by </b><i><a class="txt" href="#E1:28_1_1_1"><i><font color="Green" title="E28">A1</font></i></a>, <a class="txt" href="#E2:28_1_1_1"><i><font color="Green" title="E29">A2</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="c14">A</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"><font color="Maroon" title="c6">S</font>,<font color="Maroon" title="c7">T</font></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span><b> such that </b><br/><a NAME="E9:28_1_1_1"/><i><font color="Green" title="E33">A6</font></i>: 
<font color="Maroon" title="c13">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <font color="Maroon" title="c14">A</font>
 <b>and </b><br/><a NAME="E10:28_1_1_1"/><i><font color="Green" title="E34">A7</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="c14">A</font> holds <br/> ex <font color="Olive" title="b2">X1</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c6">S</font> ex <font color="Olive" title="b3">Y1</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c7">T</font> 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="#E6:28_1_1_1"><i><font color="Green" title="E31">A4</font></i></a>, <a class="ref" href="borsuk_1.html#T45" title="BORSUK_1:th.45">BORSUK_1:45</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c15">e</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E12:28_1_1_1"/><i><font color="Green" title="E35">A8</font></i>: 
<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c11">p</font>,<font color="Maroon" title="c10">t</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="c15">e</font>
 <b>and </b><br/><a NAME="E13:28_1_1_1"/><i><font color="Green" title="E36">A9</font></i>: 
<font color="Maroon" title="c15">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">A</font>
 <b>by </b><i><a class="txt" href="#E5:28_1_1_1"><i><font color="Green" title="E30">A3</font></i></a>, <a class="txt" href="#E9:28_1_1_1"><i><font color="Green" title="E33">A6</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="c16">X1</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c6">S</font>, <font color="Maroon" title="c17">Y1</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c7">T</font><b> such that </b><br/><a NAME="E15:28_1_1_1"/><i><font color="Green" title="E37">A10</font></i>: 
<font color="Maroon" title="c15">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="Maroon" title="c16">X1</font>,<font color="Maroon" title="c17">Y1</font></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span>
 <b>and </b><br/><a NAME="E16:28_1_1_1"/><i><font color="Green" title="E38">A11</font></i>: 
<font color="Maroon" title="c16">X1</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>
 <b>and </b><br/><a NAME="E17:28_1_1_1"/>
<font color="Maroon" title="c17">Y1</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>
 <b>by </b><i><a class="txt" href="#E10:28_1_1_1"><i><font color="Green" title="E34">A7</font></i></a>, <a class="txt" href="#E13:28_1_1_1"><i><font color="Green" title="E36">A9</font></i></a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c16">X1</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c11">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c16">X1</font> &amp; <font color="Maroon" title="c16">X1</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> &amp; <span class="p1">(<span class="default"><a href="topalg_5.html#K3" title="TOPALG_5:func.3">Prj1</a> <font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c9">H</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c16">X1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c12">V</font> )</span><br/>

<b>thus </b><a NAME="E18:28_1_1_1"/>
<font color="Maroon" title="c11">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c16">X1</font>
 <b>by </b><i><a class="txt" href="#E12:28_1_1_1"><i><font color="Green" title="E35">A8</font></i></a>, <a class="txt" href="#E15:28_1_1_1"><i><font color="Green" title="E37">A10</font></i></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</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="c16">X1</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> &amp; <span class="p1">(<span class="default"><a href="topalg_5.html#K3" title="TOPALG_5:func.3">Prj1</a> <font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c9">H</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c16">X1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c12">V</font> )</span><br/>

<b>thus </b><a NAME="E19:28_1_1_1"/>
<font color="Maroon" title="c16">X1</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>
 <b>by </b><i><a class="txt" href="#E16:28_1_1_1"><i><font color="Green" title="E38">A11</font></i></a></i>; <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="topalg_5.html#K3" title="TOPALG_5:func.3">Prj1</a> <font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c9">H</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c16">X1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c12">V</font></span><br/>

<b>let </b><font color="Maroon" title="c18">x</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="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="topalg_5.html#K3" title="TOPALG_5:func.3">Prj1</a> <font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c9">H</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c16">X1</font> or <font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">V</font> )</span><br/>

<b>assume </b><a NAME="E20:28_1_1_1"/>
<font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="topalg_5.html#K3" title="TOPALG_5:func.3">Prj1</a> <font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c9">H</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c16">X1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">V</font></span><br/>

<b>then consider </b><font color="Maroon" title="c19">c</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c6">S</font><b> such that </b><br/><a NAME="E22:28_1_1_1"/><i><font color="Green" title="E39">A12</font></i>: 
<font color="Maroon" title="c19">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c16">X1</font>
 <b>and </b><br/><a NAME="E23:28_1_1_1"/><i><font color="Green" title="E40">A13</font></i>: 
<font color="Maroon" title="c18">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="topalg_5.html#K3" title="TOPALG_5:func.3">Prj1</a> <font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c9">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">c</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T116" title="FUNCT_2:th.116">FUNCT_2:116</a></i>;<br/>
<i><font color="Green" title="E41">A14</font></i>: <span class="p1">(<span class="default"><a href="topalg_5.html#K3" title="TOPALG_5:func.3">Prj1</a> <font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c9">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">c</font> = 
<font color="Maroon" title="c9">H</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c19">c</font>,<font color="Maroon" title="c10">t</font>
<b>by </b><i><a class="ref" href="topalg_5.html#D2" target="_self" title="TOPALG_5:def.2">Def2</a></i>
<br/>.= 
<font color="Maroon" title="c9">H</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="c19">c</font>,<font color="Maroon" title="c10">t</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>

;<br/>
<a NAME="E25:28_1_1_1"/>
<font color="Maroon" title="c10">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c17">Y1</font>
 
<b>by </b><i><a class="txt" href="#E12:28_1_1_1"><i><font color="Green" title="E35">A8</font></i></a>, <a class="txt" href="#E15:28_1_1_1"><i><font color="Green" title="E37">A10</font></i></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/>
<a NAME="E26:28_1_1_1"/><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="c19">c</font>,<font color="Maroon" title="c10">t</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"><font color="Maroon" title="c16">X1</font>,<font color="Maroon" title="c17">Y1</font></span><a href="borsuk_1.html#K5" title="BORSUK_1:func.5">:]</a></span>
 
<b>by </b><i><a class="txt" href="#E22:28_1_1_1"><i><font color="Green" title="E39">A12</font></i></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/>
<a NAME="E27:28_1_1_1"/><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="c19">c</font>,<font color="Maroon" title="c10">t</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="c13">W</font>
 
<b>by </b><i><a class="txt" href="#E9:28_1_1_1"><i><font color="Green" title="E33">A6</font></i></a>, <a class="txt" href="#E13:28_1_1_1"><i><font color="Green" title="E36">A9</font></i></a>, <a class="txt" href="#E15:28_1_1_1"><i><font color="Green" title="E37">A10</font></i></a>, <a class="ref" href="tarski.html#D4" title="TARSKI:def.4">TARSKI:def 4</a></i>;<br/>
<a NAME="E28:28_1_1_1"/><b>then </b>
<font color="Maroon" title="c9">H</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="c19">c</font>,<font color="Maroon" title="c10">t</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="c9">H</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c13">W</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#T43" title="FUNCT_2:th.43">FUNCT_2:43</a></i>;<br/>
<b>hence </b><a NAME="E29:28_1_1_1"/>
<font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">V</font>
 <b>by </b><i><a class="txt" href="#E7:28_1_1_1"><i><font color="Green" title="E32">A5</font></i></a>, <a class="txt" href="#E23:28_1_1_1"><i><font color="Green" title="E40">A13</font></i></a>, <a class="txt" href="#E24:28_1_1_1"><i><font color="Green" title="E41">A14</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>hence </b><a NAME="E2:28_1_1"/>
 <a href="topalg_5.html#K3" title="TOPALG_5:func.3">Prj1</a> <font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c9">H</font> is <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>
 <b>by </b><i><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>
