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<b>reconsider </b><font color="Maroon">f1</font> =  <a href="grcat_1.html#K7">id</a> <a href="topmetr.html#K5">I[01]</a>  as   <a href="struct_0.html#NM6">Function</a> of <a href="topmetr.html#K5">I[01]</a> ,<a href="topalg_2.html#K3">R^1</a>  <b>by </b><i><a class="ref" href="funct_2.html#T9">FUNCT_2:9</a>, <a class="ref" href="topmetr.html#T24">TOPMETR:24</a>, <a class="ref" href="borsuk_1.html#T83">BORSUK_1:83</a></i>;<br/>
<a NAME="E2:25_1_1"/>
<font color="Maroon">f1</font> is <a href="pre_topc.html#V5">continuous</a>
 
<b>by </b><i><a class="ref" href="topmetr.html#T7">TOPMETR:7</a></i>;<br/>
<b>then consider </b><font color="Maroon">g</font> being   <a href="struct_0.html#NM6">Function</a> of <a href="topmetr.html#K5">I[01]</a> ,<a href="topalg_2.html#K3">R^1</a> <b> such that </b><br/><a NAME="E4:25_1_1"/><i><font color="Green">E72</font></i>: 
for <font color="Olive">p</font> being  <a href="pre_topc.html#NM2">Point</a> of <a href="topmetr.html#K5">I[01]</a> <br/> for <font color="Olive">r1</font> being <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a>   st <font color="Maroon">f1</font> <a href="funct_2.html#K3">.</a> <font color="Olive">p</font> <a href="hidden.html#R1">=</a> <font color="Olive">r1</font> holds <br/><font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Olive">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">r</font> <a href="xcmplx_0.html#K3">*</a> <font color="Olive">r1</font>
 <b>and </b><br/><a NAME="E5:25_1_1"/><i><font color="Green">E73</font></i>: 
<font color="Maroon">g</font> is <a href="pre_topc.html#V5">continuous</a>
 <b>by </b><i><a class="ref" href="jgraph_2.html#T33">JGRAPH_2:33</a></i>;<br/>
<a NAME="E6:25_1_1"/>
for <font color="Olive">x</font> being  <a href="pre_topc.html#NM2">Point</a> of <a href="topmetr.html#K5">I[01]</a>  holds  <font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="topalg_5.html#K1" target="_self">ExtendInt</a> <font color="Maroon">r</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Olive">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be   <a href="pre_topc.html#NM2">Point</a> of <a href="topmetr.html#K5">I[01]</a> ;<br/>

<b>thus </b><font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> = 
<font color="Maroon">r</font> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">f1</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">r</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="funct_1.html#T35">FUNCT_1:35</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="topalg_5.html#K1" target="_self">ExtendInt</a> <font color="Maroon">r</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font>
<b>by </b><i/>
;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E7:25_1_1"/>
 <a href="topalg_5.html#K1" target="_self">ExtendInt</a> <font color="Maroon">r</font> is <a href="pre_topc.html#V5">continuous</a>
 <b>by </b><i>, <a class="ref" href="funct_2.html#T113">FUNCT_2:113</a></i>;<br/>


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