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

<b>set </b><font color="Maroon">IT</font> = <a href="topmetr.html#K5">I[01]</a>  <a href="borsuk_1.html#K3">--&gt;</a> <font color="Maroon">a</font>;<br/>
<a NAME="E1:22_1_1"/><i><font color="Green">E32</font></i>: 
<a href="topmetr.html#K5">I[01]</a>  <a href="borsuk_1.html#K3">--&gt;</a> <font color="Maroon">a</font> <a href="funct_2.html#R2">=</a> the <a href="struct_0.html#U1">carrier</a> of <a href="topmetr.html#K5">I[01]</a>  <a href="borsuk_1.html#K1">--&gt;</a> <font color="Maroon">a</font>
 
<b>by </b><i><a class="ref" href="borsuk_1.html#D2">BORSUK_1:def 2</a></i>;<br/>
<a NAME="E2:22_1_1"/><i><font color="Green">E33</font></i>: 
( <span class="p1">(<span class="default"><a href="topmetr.html#K5">I[01]</a>  <a href="borsuk_1.html#K3">--&gt;</a> <font color="Maroon">a</font></span>)</span> <a href="funct_1.html#K1">.</a> 0 <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <span class="p1">(<span class="default"><a href="topmetr.html#K5">I[01]</a>  <a href="borsuk_1.html#K3">--&gt;</a> <font color="Maroon">a</font></span>)</span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> )
 
<b>by </b><i>, <a class="ref" href="borsuk_1.html#D17">BORSUK_1:def 17</a>, <a class="ref" href="borsuk_1.html#D18">BORSUK_1:def 18</a>, <a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>;<br/>
<a NAME="E3:22_1_1"/>
<font color="Maroon">a</font>,<font color="Maroon">a</font> <a href="borsuk_2.html#R2" target="_self">are_connected</a> 
 
;<br/>
<b>then reconsider </b><font color="Maroon">IT</font> = <a href="topmetr.html#K5">I[01]</a>  <a href="borsuk_1.html#K3">--&gt;</a> <font color="Maroon">a</font> as    <a href="borsuk_2.html#M1" target="_self">Path</a> of <font color="Maroon">a</font>,<font color="Maroon">a</font> <b>by </b><i>, </i>;<br/>
<a NAME="E5:22_1_1"/>
for <font color="Olive">n1</font>, <font color="Olive">n2</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">n1</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">IT</font> &amp; <font color="Olive">n2</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">IT</font> holds <br/><font color="Maroon">IT</font> <a href="funct_1.html#K1">.</a> <font color="Olive">n1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">IT</font> <a href="funct_1.html#K1">.</a> <font color="Olive">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">n1</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">n2</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:22_1_1_1"/>
( <font color="Maroon">n1</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">IT</font> &amp; <font color="Maroon">n2</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">IT</font> )
 ;<br/>

<a NAME="E2:22_1_1_1"/><b>then </b><i><font color="Green">E36</font></i>: 
( <font color="Maroon">n1</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <a href="topmetr.html#K5">I[01]</a>  &amp; <font color="Maroon">n2</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <a href="topmetr.html#K5">I[01]</a>  )
 
;<br/>
<b>then </b><font color="Maroon">IT</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n1</font> = 
<font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>
<br/>.= 
<font color="Maroon">IT</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n2</font>
<b>by </b><i>, , <a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>
;<br/>
<b>hence </b><a NAME="E4:22_1_1_1"/>
<font color="Maroon">IT</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">IT</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n2</font>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E6:22_1_1"/><b>then </b>
<font color="Maroon">IT</font> is <a href="funct_1.html#V3">constant</a>
 
<b>by </b><i><a class="ref" href="funct_1.html#D16">FUNCT_1:def 16</a></i>;<br/>
<b>hence </b><a NAME="E7:22_1_1"/>
 ex <font color="Olive">b<sub>1</sub></font> being   <a href="borsuk_2.html#M1" target="_self">Path</a> of <font color="Maroon">a</font>,<font color="Maroon">a</font> st <font color="Olive">b<sub>1</sub></font> is <a href="funct_1.html#V3">constant</a>
 ;<br/>


</div>
