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<b>let </b><font color="Maroon" title="c5">S</font>, <font color="Maroon" title="c6">T</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/><b>let </b><font color="Maroon" title="c7">s</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c5">S</font>;<br/><b>let </b><font color="Maroon" title="c8">f</font> be  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a> <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c5">S</font>,<font color="Maroon" title="c6">T</font>;<br/><b>let </b><font color="Maroon" title="c9">ls</font> be   <a href="topalg_1.html#NM1" title="TOPALG_1:NM.1">Loop</a> of <font color="Maroon" title="c7">s</font>;<br/>







<b>reconsider </b><font color="Maroon" title="c10">x</font> =  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <span class="p1">(<span class="default"><a href="topalg_1.html#K2" title="TOPALG_1:func.2">EqRel</a> <font color="Maroon" title="c5">S</font>,<font color="Maroon" title="c7">s</font></span>)</span>,<font color="Maroon" title="c9">ls</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="topalg_1.html#NK4" title="TOPALG_1:NK.4">pi_1</a> <font color="Maroon" title="c5">S</font>,<font color="Maroon" title="c7">s</font></span>)</span> <b>by </b><i><a class="ref" href="topalg_1.html#T48" title="TOPALG_1:th.48">TOPALG_1:48</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c11">ls1</font> being   <a href="topalg_1.html#NM1" title="TOPALG_1:NM.1">Loop</a> of <font color="Maroon" title="c7">s</font><b> such that </b><br/><a NAME="E3:39"/><i><font color="Green" title="E16">A1</font></i>: 
<font color="Maroon" title="c10">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <span class="p1">(<span class="default"><a href="topalg_1.html#K2" title="TOPALG_1:func.2">EqRel</a> <font color="Maroon" title="c5">S</font>,<font color="Maroon" title="c7">s</font></span>)</span>,<font color="Maroon" title="c11">ls1</font>
 <b>and </b><br/><a NAME="E4:39"/><i><font color="Green" title="E17">A2</font></i>: 
<span class="p1">(<span class="default"><a href="topalg_3.html#K3" title="TOPALG_3:func.3">FundGrIso</a> <font color="Maroon" title="c8">f</font>,<font color="Maroon" title="c7">s</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <span class="p1">(<span class="default"><a href="topalg_1.html#K2" title="TOPALG_1:func.2">EqRel</a> <font color="Maroon" title="c6">T</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">s</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">f</font> <a href="topalg_3.html#K2" title="TOPALG_3:func.2">*</a> <font color="Maroon" title="c11">ls1</font></span>)</span>
 <b>by </b><i><a class="ref" href="topalg_3.html#D1" target="_self" title="TOPALG_3:def.1">Def1</a></i>;<br/>
<a NAME="E5:39"/>
<font color="Maroon" title="c9">ls</font>,<font color="Maroon" title="c11">ls1</font> <a href="borsuk_2.html#R3" title="BORSUK_2:pred.3">are_homotopic</a> 
 
<b>by </b><i><a class="txt" href="topalg_3.html#E3:39"><i><font color="Green" title="E16">A1</font></i></a>, <a class="ref" href="topalg_1.html#T47" title="TOPALG_1:th.47">TOPALG_1:47</a></i>;<br/>
<a NAME="E6:39"/><b>then </b>
<font color="Maroon" title="c8">f</font> <a href="topalg_3.html#K2" title="TOPALG_3:func.2">*</a> <font color="Maroon" title="c9">ls</font>,<font color="Maroon" title="c8">f</font> <a href="topalg_3.html#K2" title="TOPALG_3:func.2">*</a> <font color="Maroon" title="c11">ls1</font> <a href="borsuk_2.html#R3" title="BORSUK_2:pred.3">are_homotopic</a> 
 
<b>by </b><i><a class="ref" href="topalg_3.html#T28" target="_self" title="TOPALG_3:th.28">Th28</a></i>;<br/>
<b>hence </b><a NAME="E7:39"/>
<span class="p1">(<span class="default"><a href="topalg_3.html#K3" title="TOPALG_3:func.3">FundGrIso</a> <font color="Maroon" title="c8">f</font>,<font color="Maroon" title="c7">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <span class="p2">(<span class="default"><a href="topalg_1.html#K2" title="TOPALG_1:func.2">EqRel</a> <font color="Maroon" title="c5">S</font>,<font color="Maroon" title="c7">s</font></span>)</span>,<font color="Maroon" title="c9">ls</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <span class="p1">(<span class="default"><a href="topalg_1.html#K2" title="TOPALG_1:func.2">EqRel</a> <font color="Maroon" title="c6">T</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">s</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">f</font> <a href="topalg_3.html#K2" title="TOPALG_3:func.2">*</a> <font color="Maroon" title="c9">ls</font></span>)</span>
 <b>by </b><i><a class="txt" href="topalg_3.html#E4:39"><i><font color="Green" title="E17">A2</font></i></a>, <a class="ref" href="topalg_1.html#T47" title="TOPALG_1:th.47">TOPALG_1:47</a></i>;<br/>


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