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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#V3" title="STRUCT_0:attr.3">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">x</font> be   <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>;<br/><b>let </b><font color="Maroon" title="c10">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>let </b><font color="Maroon" title="c11">lt</font> be   <a href="topalg_1.html#NM1" title="TOPALG_1:NM.1">Loop</a> of <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>;<br/>











<b>assume </b><b>that </b><br/><a NAME="E1:37"/><i><font color="Green" title="E16">A1</font></i>: 
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K7" title="EQREL_1:func.7">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="c10">ls</font>
 <b>and </b><br/><a NAME="E2:37"/><i><font color="Green" title="E17">A2</font></i>: 
<font color="Maroon" title="c11">lt</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c8">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c10">ls</font>
 ;<br/>

<b>consider </b><font color="Maroon" title="c12">ls1</font> being   <a href="topalg_1.html#NM1" title="TOPALG_1:NM.1">Loop</a> of <font color="Maroon" title="c7">s</font>, <font color="Maroon" title="c13">lt1</font> being   <a href="topalg_1.html#NM1" title="TOPALG_1:NM.1">Loop</a> of <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><b> such that </b><br/><a NAME="E4:37"/><i><font color="Green" title="E18">A3</font></i>: 
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K7" title="EQREL_1:func.7">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="c12">ls1</font>
 <b>and </b><br/><a NAME="E5:37"/><i><font color="Green" title="E19">A4</font></i>: 
<font color="Maroon" title="c13">lt1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c8">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c12">ls1</font>
 <b>and </b><br/><a NAME="E6:37"/><i><font color="Green" title="E20">A5</font></i>: 
<span class="p1">(<span class="default"><a href="topalg_3.html#K1" title="TOPALG_3:func.1">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="c9">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K7" title="EQREL_1:func.7">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>,<font color="Maroon" title="c13">lt1</font>
 <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="E7:37"/>
<font color="Maroon" title="c10">ls</font>,<font color="Maroon" title="c12">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#E1:37"><i><font color="Green" title="E16">A1</font></i></a>, <a class="txt" href="topalg_3.html#E4:37"><i><font color="Green" title="E18">A3</font></i></a>, <a class="ref" href="topalg_1.html#T47" title="TOPALG_1:th.47">TOPALG_1:47</a></i>;<br/>
<a NAME="E8:37"/><b>then </b>
<font color="Maroon" title="c11">lt</font>,<font color="Maroon" title="c13">lt1</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#E2:37"><i><font color="Green" title="E17">A2</font></i></a>, <a class="txt" href="topalg_3.html#E5:37"><i><font color="Green" title="E19">A4</font></i></a>, <a class="ref" href="topalg_3.html#T28" target="_self" title="TOPALG_3:th.28">Th28</a></i>;<br/>
<b>hence </b><a NAME="E9:37"/>
<span class="p1">(<span class="default"><a href="topalg_3.html#K1" title="TOPALG_3:func.1">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="c9">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K7" title="EQREL_1:func.7">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>,<font color="Maroon" title="c11">lt</font>
 <b>by </b><i><a class="txt" href="topalg_3.html#E6:37"><i><font color="Green" title="E20">A5</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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