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<b>let </b><font color="Maroon">S</font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>, <font color="Maroon">T</font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">s</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">f</font> be  <a href="pre_topc.html#V5">continuous</a> <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">S</font>,<font color="Maroon">T</font>;<br/><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="topalg_1.html#NK4" target="_self">pi_1</a> <font color="Maroon">S</font>,<font color="Maroon">s</font></span>)</span>;<br/><b>let </b><font color="Maroon">ls</font> be   <a href="topalg_1.html#NM1">Loop</a> of <font color="Maroon">s</font>;<br/><b>let </b><font color="Maroon">lt</font> be   <a href="topalg_1.html#NM1">Loop</a> of <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">s</font>;<br/>











<b>assume </b><b>that </b><br/><a NAME="E1:37"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="topalg_1.html#K2">EqRel</a> <font color="Maroon">S</font>,<font color="Maroon">s</font></span>)</span>,<font color="Maroon">ls</font>
 <b>and </b><br/><a NAME="E2:37"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">lt</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">f</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">ls</font>
 ;<br/>

<b>consider </b><font color="Maroon">ls1</font> being   <a href="topalg_1.html#NM1">Loop</a> of <font color="Maroon">s</font>, <font color="Maroon">lt1</font> being   <a href="topalg_1.html#NM1">Loop</a> of <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">s</font><b> such that </b><br/><a NAME="E4:37"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="topalg_1.html#K2">EqRel</a> <font color="Maroon">S</font>,<font color="Maroon">s</font></span>)</span>,<font color="Maroon">ls1</font>
 <b>and </b><br/><a NAME="E5:37"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">lt1</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">f</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">ls1</font>
 <b>and </b><br/><a NAME="E6:37"/><i><font color="Green">E50</font></i>: 
<span class="p1">(<span class="default"><a href="topalg_3.html#K1" target="_self">FundGrIso</a> <font color="Maroon">f</font>,<font color="Maroon">s</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="topalg_1.html#K2">EqRel</a> <font color="Maroon">T</font>,<span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">s</font></span>)</span></span>)</span>,<font color="Maroon">lt1</font>
 <b>by </b><i/>;<br/>
<a NAME="E7:37"/>
<font color="Maroon">ls</font>,<font color="Maroon">ls1</font> <a href="borsuk_2.html#R3">are_homotopic</a> 
 
<b>by </b><i>, , <a class="ref" href="topalg_1.html#T47">TOPALG_1:47</a></i>;<br/>
<a NAME="E8:37"/><b>then </b>
<font color="Maroon">lt</font>,<font color="Maroon">lt1</font> <a href="borsuk_2.html#R3">are_homotopic</a> 
 
<b>by </b><i>, , </i>;<br/>
<b>hence </b><a NAME="E9:37"/>
<span class="p1">(<span class="default"><a href="topalg_3.html#K1" target="_self">FundGrIso</a> <font color="Maroon">f</font>,<font color="Maroon">s</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="topalg_1.html#K2">EqRel</a> <font color="Maroon">T</font>,<span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">s</font></span>)</span></span>)</span>,<font color="Maroon">lt</font>
 <b>by </b><i>, <a class="ref" href="topalg_1.html#T47">TOPALG_1:47</a></i>;<br/>


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