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<b>let </b><font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></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">c<sub>7</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>5</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>8</sub></font> be  <a href="pre_topc.html#V5">continuous</a> <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>9</sub></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">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span>;<br/><b>let </b><font color="Maroon">c<sub>10</sub></font> be   <a href="topalg_1.html#NM1">Loop</a> of <font color="Maroon">c<sub>7</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>11</sub></font> be   <a href="topalg_1.html#NM1">Loop</a> of <font color="Maroon">c<sub>8</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>7</sub></font>;<br/>











<b>assume </b><b>that </b><br/><a NAME="E1:37"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>9</sub></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">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span>,<font color="Maroon">c<sub>10</sub></font>
 <b>and </b><br/><a NAME="E2:37"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#R2">=</a> <font color="Maroon">c<sub>8</sub></font> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>10</sub></font>
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>12</sub></font> being   <a href="topalg_1.html#NM1">Loop</a> of <font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>13</sub></font> being   <a href="topalg_1.html#NM1">Loop</a> of <font color="Maroon">c<sub>8</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>7</sub></font><b> such that </b><br/><a NAME="E4:37"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>9</sub></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">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span>,<font color="Maroon">c<sub>12</sub></font>
 <b>and </b><br/><a NAME="E5:37"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">c<sub>13</sub></font> <a href="funct_2.html#R2">=</a> <font color="Maroon">c<sub>8</sub></font> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>12</sub></font>
 <b>and </b><br/><a NAME="E6:37"/><i><font color="Green">E20</font></i>: 
<span class="p1">(<span class="default"><a href="topalg_3.html#K1" target="_self">FundGrIso</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></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">c<sub>6</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="ref" href="topalg_3.html#D1" target="_self">Def1</a></i>;<br/>
<a NAME="E7:37"/>
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="borsuk_2.html#R3">are_homotopic</a> 
 
<b>by </b><i><a class="txt" href="topalg_3.html#E1:37"><i><font color="Green">E16</font></i></a>, <a class="txt" href="topalg_3.html#E4:37"><i><font color="Green">E18</font></i></a>, <a class="ref" href="topalg_1.html#T47">TOPALG_1:47</a></i>;<br/>
<a NAME="E8:37"/><b>then </b>
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="borsuk_2.html#R3">are_homotopic</a> 
 
<b>by </b><i><a class="txt" href="topalg_3.html#E2:37"><i><font color="Green">E17</font></i></a>, <a class="txt" href="topalg_3.html#E5:37"><i><font color="Green">E19</font></i></a>, <a class="ref" href="topalg_3.html#T28" target="_self">Th28</a></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">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></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">c<sub>6</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>11</sub></font>
 <b>by </b><i><a class="txt" href="topalg_3.html#E6:37"><i><font color="Green">E20</font></i></a>, <a class="ref" href="topalg_1.html#T47">TOPALG_1:47</a></i>;<br/>


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