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<b>let </b><font color="Maroon">R</font> be    <a href="borsuk_2.html#M1" target="_self">Path</a> of <font color="Maroon">b</font>,<font color="Maroon">a</font>, <font color="Maroon">Q</font> be    <a href="borsuk_2.html#M1" target="_self">Path</a> of <font color="Maroon">b</font>,<font color="Maroon">a</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:26_1_2"/><i><font color="Green">E54</font></i>: 
for <font color="Olive">t</font> being  <a href="pre_topc.html#NM2">Point</a> of <a href="topmetr.html#K5">I[01]</a>  holds  <font color="Maroon">R</font> <a href="funct_2.html#K3">.</a> <font color="Olive">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">P</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <font color="Olive">t</font></span>)</span>
 <b>and </b><br/><a NAME="E2:26_1_2"/><i><font color="Green">E55</font></i>: 
for <font color="Olive">t</font> being  <a href="pre_topc.html#NM2">Point</a> of <a href="topmetr.html#K5">I[01]</a>  holds  <font color="Maroon">Q</font> <a href="funct_2.html#K3">.</a> <font color="Olive">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">P</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <font color="Olive">t</font></span>)</span>
 ;<br/>

<a NAME="E3:26_1_2"/><i><font color="Green">E56</font></i>: 
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">R</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <a href="topmetr.html#K5">I[01]</a> 
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E4:26_1_2"/><i><font color="Green">E57</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <a href="topmetr.html#K5">I[01]</a>  <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">Q</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E5:26_1_2"/>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</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>  holds <br/><font color="Maroon">R</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">Q</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:26_1_2_1"/>
<font color="Maroon">x</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 reconsider </b><font color="Maroon">x'</font> = <font color="Maroon">x</font> as   <a href="pre_topc.html#NM2">Point</a> of <a href="topmetr.html#K5">I[01]</a>  ;<br/>
<font color="Maroon">R</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x'</font> = 
<font color="Maroon">P</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">x'</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">Q</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x'</font>
<b>by </b><i/>
;<br/>
<b>hence </b><a NAME="E4:26_1_2_1"/>
<font color="Maroon">R</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">Q</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E6:26_1_2"/>
<font color="Maroon">R</font> <a href="hidden.html#R1">=</a> <font color="Maroon">Q</font>
 <b>by </b><i>, , <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>


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