<?xml version="1.0"?>
<div class="add">

<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>assume </b><a NAME="E1:39"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>8</sub></font> is <a href="tops_2.html#V3">being_homeomorphism</a>
 ;<br/>

<b>set </b><font color="Maroon">c<sub>9</sub></font> =  <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>;<br/>
<b>set </b><font color="Maroon">c<sub>10</sub></font> =  <a href="topalg_1.html#NK4" target="_self">pi_1</a> <font color="Maroon">c<sub>6</sub></font>,<span class="p1">(<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>;<br/>
<a NAME="E2:39"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="tops_2.html#NK3" target="_self">"</a>  is <a href="pre_topc.html#V5">continuous</a>
 
<b>by </b><i><a class="txt" href="topalg_3.html#E1:39"><i><font color="Green">E17</font></i></a>, <a class="ref" href="tops_2.html#D5">TOPS_2:def 5</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>11</sub></font> =  <a href="topalg_3.html#K2" target="_self">FundGrIso</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font>;<br/>
<a NAME="E3:39"/><i><font color="Green">E19</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="topalg_3.html#K2" target="_self">FundGrIso</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</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>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E4:39"/><i><font color="Green">E20</font></i>: 
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="topalg_3.html#E1:39"><i><font color="Green">E17</font></i></a>, <a class="ref" href="tops_2.html#D5">TOPS_2:def 5</a></i>;<br/>
<a NAME="E5:39"/><i><font color="Green">E21</font></i>: 
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="topalg_3.html#E1:39"><i><font color="Green">E17</font></i></a>, <a class="ref" href="tops_2.html#D5">TOPS_2:def 5</a></i>;<br/>
<a NAME="E6:39"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>8</sub></font> is <a href="funct_1.html#V2">one-to-one</a>
 
<b>by </b><i><a class="txt" href="topalg_3.html#E1:39"><i><font color="Green">E17</font></i></a>, <a class="ref" href="tops_2.html#D5">TOPS_2:def 5</a></i>;<br/>
<a NAME="E7:39"/><b>then </b><i><font color="Green">E23</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="funct_1.html#K2">"</a> </span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<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> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="ref" href="funct_2.html#T32">FUNCT_2:32</a></i>;<br/>
<a NAME="E8:39"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="funct_1.html#K2">"</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> <a href="tops_2.html#NK3" target="_self">"</a> 
 
<b>by </b><i><a class="txt" href="topalg_3.html#E5:39"><i><font color="Green">E21</font></i></a>, <a class="txt" href="topalg_3.html#E6:39"><i><font color="Green">E22</font></i></a>, <a class="ref" href="tops_2.html#D4">TOPS_2:def 4</a></i>;<br/>
<a NAME="E9:39"/><i><font color="Green">E25</font></i>: 
 <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="topalg_3.html#K2" target="_self">FundGrIso</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="topalg_1.html#NK4" target="_self">pi_1</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>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:39_1"/>
 <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="topalg_3.html#K2" target="_self">FundGrIso</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="topalg_1.html#NK4" target="_self">pi_1</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>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/>

<b>let </b><font color="Maroon">c<sub>12</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E2:39_1"/>
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="topalg_1.html#NK4" target="_self">pi_1</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>
 ;<br/>

<b>then consider </b><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="E4:39_1"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>12</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_1.html#T48">TOPALG_1:48</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>14</sub></font> = <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="tops_2.html#NK3" target="_self">"</a> </span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>13</sub></font> as   <a href="topalg_1.html#NM1">Loop</a> of <font color="Maroon">c<sub>7</sub></font> <b>by </b><i><a class="txt" href="topalg_3.html#E2:39"><i><font color="Green">E18</font></i></a>, <a class="txt" href="topalg_3.html#E7:39"><i><font color="Green">E23</font></i></a>, <a class="txt" href="topalg_3.html#E8:39"><i><font color="Green">E24</font></i></a>, <a class="ref" href="topalg_3.html#T27" target="_self">Th27</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>15</sub></font> =  <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>14</sub></font>;<br/>
<a NAME="E6:39_1"/><i><font color="Green">E27</font></i>: 
 <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>14</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</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>
 
<b>by </b><i><a class="ref" href="topalg_1.html#T48">TOPALG_1:48</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>16</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>17</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="E8:39_1"/><i><font color="Green">E28</font></i>: 
 <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>14</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>16</sub></font>
 <b>and </b><br/><a NAME="E9:39_1"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>17</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>16</sub></font>
 <b>and </b><br/><a NAME="E10:39_1"/><i><font color="Green">E30</font></i>: 
<span class="p1">(<span class="default"><a href="topalg_3.html#K2" 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_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="eqrel_1.html#K7">Class</a> <span class="p2">(<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>14</sub></font></span>)</span> <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>17</sub></font>
 <b>by </b><i><a class="ref" href="topalg_3.html#D1" target="_self">Def1</a></i>;<br/>
<i><font color="Green">E31</font></i>: <font color="Maroon">c<sub>8</sub></font> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>14</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="tops_2.html#NK3" target="_self">"</a> </span>)</span></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>13</sub></font>
<b>by </b><i><a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p2">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>13</sub></font>
<b>by </b><i><a class="txt" href="topalg_3.html#E5:39"><i><font color="Green">E21</font></i></a>, <a class="txt" href="topalg_3.html#E6:39"><i><font color="Green">E22</font></i></a>, <a class="ref" href="tops_2.html#T65">TOPS_2:65</a></i>
<br/>.= 
<font color="Maroon">c<sub>13</sub></font>
<b>by </b><i><a class="txt" href="topalg_3.html#E5:39"><i><font color="Green">E21</font></i></a>, <a class="ref" href="funct_2.html#T23">FUNCT_2:23</a></i>
;<br/>
<a NAME="E12:39_1"/>
<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>16</sub></font> <a href="borsuk_2.html#R3">are_homotopic</a> 
 
<b>by </b><i><a class="txt" href="topalg_3.html#E8:39_1"><i><font color="Green">E28</font></i></a>, <a class="ref" href="topalg_1.html#T47">TOPALG_1:47</a></i>;<br/>
<a NAME="E13:39_1"/><b>then </b>
<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>17</sub></font> <a href="borsuk_2.html#R3">are_homotopic</a> 
 
<b>by </b><i><a class="txt" href="topalg_3.html#E9:39_1"><i><font color="Green">E29</font></i></a>, <a class="txt" href="topalg_3.html#E11:39_1"><i><font color="Green">E31</font></i></a>, <a class="ref" href="topalg_3.html#T28" target="_self">Th28</a></i>;<br/>
<a NAME="E14:39_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="topalg_3.html#K2" 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_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="eqrel_1.html#K7">Class</a> <span class="p2">(<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>14</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>12</sub></font>
 
<b>by </b><i><a class="txt" href="topalg_3.html#E4:39_1"><i><font color="Green">E26</font></i></a>, <a class="txt" href="topalg_3.html#E10:39_1"><i><font color="Green">E30</font></i></a>, <a class="ref" href="topalg_1.html#T47">TOPALG_1:47</a></i>;<br/>
<b>hence </b><a NAME="E15:39_1"/>
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="topalg_3.html#K2" target="_self">FundGrIso</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="topalg_3.html#E3:39"><i><font color="Green">E19</font></i></a>, <a class="txt" href="topalg_3.html#E6:39_1"><i><font color="Green">E27</font></i></a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E10:39"/>
 <a href="topalg_3.html#K2" target="_self">FundGrIso</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font> is <a href="funct_1.html#V2">one-to-one</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>12</sub></font>, <font color="Maroon">c<sub>13</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a><br/>

<b>assume </b><a NAME="E1:39_2"/>
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="topalg_3.html#K2" target="_self">FundGrIso</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>14</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>15</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="E3:39_2"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>12</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>14</sub></font>
 <b>and </b><br/><a NAME="E4:39_2"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>15</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>14</sub></font>
 <b>and </b><br/><a NAME="E5:39_2"/><i><font color="Green">E28</font></i>: 
<span class="p1">(<span class="default"><a href="topalg_3.html#K2" 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_1.html#K1">.</a> <font color="Maroon">c<sub>12</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>15</sub></font>
 <b>by </b><i><a class="ref" href="topalg_3.html#D1" target="_self">Def1</a></i>;<br/>
<b>assume </b><a NAME="E6:39_2"/>
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="topalg_3.html#K2" target="_self">FundGrIso</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>16</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>17</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="E8:39_2"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>13</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>16</sub></font>
 <b>and </b><br/><a NAME="E9:39_2"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">c<sub>17</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>16</sub></font>
 <b>and </b><br/><a NAME="E10:39_2"/><i><font color="Green">E31</font></i>: 
<span class="p1">(<span class="default"><a href="topalg_3.html#K2" 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_1.html#K1">.</a> <font color="Maroon">c<sub>13</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>17</sub></font>
 <b>by </b><i><a class="ref" href="topalg_3.html#D1" target="_self">Def1</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>18</sub></font> = <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="tops_2.html#NK3" target="_self">"</a> </span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>15</sub></font>, <font color="Maroon">c<sub>19</sub></font> = <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="tops_2.html#NK3" target="_self">"</a> </span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>17</sub></font> as   <a href="topalg_1.html#NM1">Loop</a> of <font color="Maroon">c<sub>7</sub></font> <b>by </b><i><a class="txt" href="topalg_3.html#E2:39"><i><font color="Green">E18</font></i></a>, <a class="txt" href="topalg_3.html#E7:39"><i><font color="Green">E23</font></i></a>, <a class="txt" href="topalg_3.html#E8:39"><i><font color="Green">E24</font></i></a>, <a class="ref" href="topalg_3.html#T27" target="_self">Th27</a></i>;<br/>
<a NAME="E12:39_2"/><i><font color="Green">E32</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="tops_2.html#NK3" target="_self">"</a> </span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font> <a href="funct_2.html#R1">=</a>  <a href="partfun1.html#K6">id</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="topalg_3.html#E5:39"><i><font color="Green">E21</font></i></a>, <a class="txt" href="topalg_3.html#E6:39"><i><font color="Green">E22</font></i></a>, <a class="ref" href="tops_2.html#T65">TOPS_2:65</a></i>;<br/>
<i><font color="Green">E33</font></i>: <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="tops_2.html#NK3" target="_self">"</a> </span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>15</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="tops_2.html#NK3" target="_self">"</a> </span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>14</sub></font>
<b>by </b><i><a class="txt" href="topalg_3.html#E4:39_2"><i><font color="Green">E27</font></i></a>, <a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>
<br/>.= 
<font color="Maroon">c<sub>14</sub></font>
<b>by </b><i><a class="txt" href="topalg_3.html#E4:39"><i><font color="Green">E20</font></i></a>, <a class="txt" href="topalg_3.html#E12:39_2"><i><font color="Green">E32</font></i></a>, <a class="ref" href="funct_2.html#T23">FUNCT_2:23</a></i>
;<br/>
<i><font color="Green">E34</font></i>: <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="tops_2.html#NK3" target="_self">"</a> </span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>17</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="tops_2.html#NK3" target="_self">"</a> </span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>16</sub></font>
<b>by </b><i><a class="txt" href="topalg_3.html#E9:39_2"><i><font color="Green">E30</font></i></a>, <a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>
<br/>.= 
<font color="Maroon">c<sub>16</sub></font>
<b>by </b><i><a class="txt" href="topalg_3.html#E4:39"><i><font color="Green">E20</font></i></a>, <a class="txt" href="topalg_3.html#E12:39_2"><i><font color="Green">E32</font></i></a>, <a class="ref" href="funct_2.html#T23">FUNCT_2:23</a></i>
;<br/>
<b>assume </b><a NAME="E15:39_2"/>
<span class="p1">(<span class="default"><a href="topalg_3.html#K2" 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_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="topalg_3.html#K2" 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_1.html#K1">.</a> <font color="Maroon">c<sub>13</sub></font>
 ;<br/>

<a NAME="E16:39_2"/><b>then </b>
<font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>17</sub></font> <a href="borsuk_2.html#R3">are_homotopic</a> 
 
<b>by </b><i><a class="txt" href="topalg_3.html#E5:39_2"><i><font color="Green">E28</font></i></a>, <a class="txt" href="topalg_3.html#E10:39_2"><i><font color="Green">E31</font></i></a>, <a class="ref" href="topalg_1.html#T47">TOPALG_1:47</a></i>;<br/>
<a NAME="E17:39_2"/><b>then </b>
<font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>19</sub></font> <a href="borsuk_2.html#R3">are_homotopic</a> 
 
<b>by </b><i><a class="txt" href="topalg_3.html#E2:39"><i><font color="Green">E18</font></i></a>, <a class="txt" href="topalg_3.html#E7:39"><i><font color="Green">E23</font></i></a>, <a class="txt" href="topalg_3.html#E8:39"><i><font color="Green">E24</font></i></a>, <a class="ref" href="topalg_3.html#T28" target="_self">Th28</a></i>;<br/>
<b>hence </b><a NAME="E18:39_2"/>
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="txt" href="topalg_3.html#E3:39_2"><i><font color="Green">E26</font></i></a>, <a class="txt" href="topalg_3.html#E8:39_2"><i><font color="Green">E29</font></i></a>, <a class="txt" href="topalg_3.html#E13:39_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="topalg_3.html#E14:39_2"><i><font color="Green">E34</font></i></a>, <a class="ref" href="topalg_1.html#T47">TOPALG_1:47</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E11:39"/>
 <a href="topalg_3.html#K2" target="_self">FundGrIso</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="group_6.html#NR3" target="_self">is_isomorphism</a> 
 <b>by </b><i><a class="txt" href="topalg_3.html#E9:39"><i><font color="Green">E25</font></i></a>, <a class="ref" href="group_6.html#T70">GROUP_6:70</a></i>;<br/>


</div>
