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

<b>set </b><font color="Maroon" title="c3">IT</font> = <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>  <a href="borsuk_1.html#K2" title="BORSUK_1:func.2">--&gt;</a> <font color="Maroon" title="c2">a</font>;<br/>
<a NAME="E1:22_1_1"/><i><font color="Green" title="E11">A1</font></i>: 
( <span class="p1">(<span class="default"><a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>  <a href="borsuk_1.html#K2" title="BORSUK_1:func.2">--&gt;</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> &amp; <span class="p1">(<span class="default"><a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>  <a href="borsuk_1.html#K2" title="BORSUK_1:func.2">--&gt;</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> )
 
<b>by </b><i><a class="ref" href="borsuk_1.html#D17" title="BORSUK_1:def.17">BORSUK_1:def 17</a>, <a class="ref" href="borsuk_1.html#D18" title="BORSUK_1:def.18">BORSUK_1:def 18</a>, <a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></i>;<br/>
<a NAME="E2:22_1_1"/>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c2">a</font> <a href="borsuk_2.html#R2" title="BORSUK_2:pred.2">are_connected</a> 
 
;<br/>
<b>then reconsider </b><font color="Maroon" title="c4">IT</font> = <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>  <a href="borsuk_1.html#K2" title="BORSUK_1:func.2">--&gt;</a> <font color="Maroon" title="c2">a</font> as    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c2">a</font> <b>by </b><i><a class="txt" href="borsuk_2.html#E1:22_1_1"><i><font color="Green" title="E11">A1</font></i></a>, <a class="ref" href="borsuk_2.html#D2" target="_self" title="BORSUK_2:def.2">Def2</a></i>;<br/>
<a NAME="E4:22_1_1"/>
for <font color="Olive" title="b1">n1</font>, <font color="Olive" title="b2">n2</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">n1</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="c4">IT</font> &amp; <font color="Olive" title="b2">n2</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="c4">IT</font> holds <br/><font color="Maroon" title="c4">IT</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">n1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">IT</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">n2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c5">n1</font>, <font color="Maroon" title="c6">n2</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E1:22_1_1_1"/><i><font color="Green" title="E12">A2</font></i>: 
( <font color="Maroon" title="c5">n1</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="c4">IT</font> &amp; <font color="Maroon" title="c6">n2</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="c4">IT</font> )
 ;<br/>

<b>then </b><font color="Maroon" title="c4">IT</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n1</font> = 
<font color="Maroon" title="c2">a</font>
<b>by </b><i><a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></i>
<br/>.= 
<font color="Maroon" title="c4">IT</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">n2</font>
<b>by </b><i><a class="txt" href="borsuk_2.html#E1:22_1_1_1"><i><font color="Green" title="E12">A2</font></i></a>, <a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></i>
;<br/>
<b>hence </b><a NAME="E3:22_1_1_1"/>
<font color="Maroon" title="c4">IT</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">IT</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">n2</font>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E5:22_1_1"/><b>then </b>
<font color="Maroon" title="c4">IT</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a>
 
<b>by </b><i><a class="ref" href="funct_1.html#D16" title="FUNCT_1:def.16">FUNCT_1:def 16</a></i>;<br/>
<b>hence </b><a NAME="E6:22_1_1"/>
 ex <font color="Olive">b<sub>1</sub></font> being   <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c2">a</font> st <font color="Olive">b<sub>1</sub></font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a>
 ;<br/>


</div>
