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<b>set </b><font color="Maroon" title="c8">F</font> =  <a href="topalg_4.html#K12" title="TOPALG_4:func.12">FGPrIso</a> <font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c7">t</font>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="43_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c9">a</font>, <font color="Maroon" title="c10">b</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> <span class="p2"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c5">T</font></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span>,<span class="p2"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c7">t</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="topalg_4.html#K12" title="TOPALG_4:func.12">FGPrIso</a> <font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c7">t</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c10">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="topalg_4.html#K12" title="TOPALG_4:func.12">FGPrIso</a> <font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c7">t</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">a</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="topalg_4.html#K12" title="TOPALG_4:func.12">FGPrIso</a> <font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c7">t</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">b</font></span>)</span></span><br/><b>consider </b><font color="Maroon" title="c11">la</font> being   <a href="topalg_1.html#NM1" title="TOPALG_1:NM.1">Loop</a> of <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c7">t</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span><b> such that </b><br/><a NAME="E2:43_1_1_1"/><i><font color="Green" title="E30">A1</font></i>: 
<font color="Maroon" title="c9">a</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> <span class="p2"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c5">T</font></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span>,<span class="p2"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c7">t</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span>,<font color="Maroon" title="c11">la</font>
 <b>and </b><br/><a NAME="E3:43_1_1_1"/><i><font color="Green" title="E31">A2</font></i>: 
<span class="p1">(<span class="default"><a href="topalg_4.html#K12" title="TOPALG_4:func.12">FGPrIso</a> <font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c7">t</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <span class="p3">(<span class="default"><a href="topalg_1.html#K2" title="TOPALG_1:func.2">EqRel</a> <font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c6">s</font></span>)</span>,<span class="p3">(<span class="default"><a href="topalg_4.html#K10" title="TOPALG_4:func.10">pr1</a> <font color="Maroon" title="c11">la</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <span class="p3">(<span class="default"><a href="topalg_1.html#K2" title="TOPALG_1:func.2">EqRel</a> <font color="Maroon" title="c5">T</font>,<font color="Maroon" title="c7">t</font></span>)</span>,<span class="p3">(<span class="default"><a href="topalg_4.html#K11" title="TOPALG_4:func.11">pr2</a> <font color="Maroon" title="c11">la</font></span>)</span></span>)</span></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="topalg_4.html#D2" target="_self" title="TOPALG_4:def.2">Def2</a></i>;<br/><b>consider </b><font color="Maroon" title="c12">lb</font> being   <a href="topalg_1.html#NM1" title="TOPALG_1:NM.1">Loop</a> of <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c7">t</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span><b> such that </b><br/><a NAME="E5:43_1_1_1"/><i><font color="Green" title="E32">A3</font></i>: 
<font color="Maroon" title="c10">b</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> <span class="p2"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c5">T</font></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span>,<span class="p2"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c7">t</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span>,<font color="Maroon" title="c12">lb</font>
 <b>and </b><br/><a NAME="E6:43_1_1_1"/><i><font color="Green" title="E33">A4</font></i>: 
<span class="p1">(<span class="default"><a href="topalg_4.html#K12" title="TOPALG_4:func.12">FGPrIso</a> <font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c7">t</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <span class="p3">(<span class="default"><a href="topalg_1.html#K2" title="TOPALG_1:func.2">EqRel</a> <font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c6">s</font></span>)</span>,<span class="p3">(<span class="default"><a href="topalg_4.html#K10" title="TOPALG_4:func.10">pr1</a> <font color="Maroon" title="c12">lb</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <span class="p3">(<span class="default"><a href="topalg_1.html#K2" title="TOPALG_1:func.2">EqRel</a> <font color="Maroon" title="c5">T</font>,<font color="Maroon" title="c7">t</font></span>)</span>,<span class="p3">(<span class="default"><a href="topalg_4.html#K11" title="TOPALG_4:func.11">pr2</a> <font color="Maroon" title="c12">lb</font></span>)</span></span>)</span></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="topalg_4.html#D2" target="_self" title="TOPALG_4:def.2">Def2</a></i>;<br/><b>consider </b><font color="Maroon" title="c13">lab</font> being   <a href="topalg_1.html#NM1" title="TOPALG_1:NM.1">Loop</a> of <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c7">t</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span><b> such that </b><br/><a NAME="E8:43_1_1_1"/><i><font color="Green" title="E34">A5</font></i>: 
<font color="Maroon" title="c9">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c10">b</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> <span class="p2"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c5">T</font></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span>,<span class="p2"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c7">t</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span>,<font color="Maroon" title="c13">lab</font>
 <b>and </b><br/><a NAME="E9:43_1_1_1"/><i><font color="Green" title="E35">A6</font></i>: 
<span class="p1">(<span class="default"><a href="topalg_4.html#K12" title="TOPALG_4:func.12">FGPrIso</a> <font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c7">t</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c10">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <span class="p3">(<span class="default"><a href="topalg_1.html#K2" title="TOPALG_1:func.2">EqRel</a> <font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c6">s</font></span>)</span>,<span class="p3">(<span class="default"><a href="topalg_4.html#K10" title="TOPALG_4:func.10">pr1</a> <font color="Maroon" title="c13">lab</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <span class="p3">(<span class="default"><a href="topalg_1.html#K2" title="TOPALG_1:func.2">EqRel</a> <font color="Maroon" title="c5">T</font>,<font color="Maroon" title="c7">t</font></span>)</span>,<span class="p3">(<span class="default"><a href="topalg_4.html#K11" title="TOPALG_4:func.11">pr2</a> <font color="Maroon" title="c13">lab</font></span>)</span></span>)</span></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="topalg_4.html#D2" target="_self" title="TOPALG_4:def.2">Def2</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c14">A1</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="c4">S</font>,<font color="Maroon" title="c6">s</font></span>)</span>,<span class="p1">(<span class="default"><a href="topalg_4.html#K10" title="TOPALG_4:func.10">pr1</a> <font color="Maroon" title="c11">la</font></span>)</span>, <font color="Maroon" title="c15">A2</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="c4">S</font>,<font color="Maroon" title="c6">s</font></span>)</span>,<span class="p1">(<span class="default"><a href="topalg_4.html#K10" title="TOPALG_4:func.10">pr1</a> <font color="Maroon" title="c12">lb</font></span>)</span> 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="c4">S</font>,<font color="Maroon" title="c6">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>reconsider </b><font color="Maroon" title="c16">B1</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">T</font>,<font color="Maroon" title="c7">t</font></span>)</span>,<span class="p1">(<span class="default"><a href="topalg_4.html#K11" title="TOPALG_4:func.11">pr2</a> <font color="Maroon" title="c11">la</font></span>)</span>, <font color="Maroon" title="c17">B2</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">T</font>,<font color="Maroon" title="c7">t</font></span>)</span>,<span class="p1">(<span class="default"><a href="topalg_4.html#K11" title="TOPALG_4:func.11">pr2</a> <font color="Maroon" title="c12">lb</font></span>)</span> 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">T</font>,<font color="Maroon" title="c7">t</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/><a NAME="E12:43_1_1_1"/>
<font color="Maroon" title="c9">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c10">b</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> <span class="p2"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c5">T</font></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span>,<span class="p2"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c7">t</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c11">la</font> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Maroon" title="c12">lb</font></span>)</span>
 <b>by </b><i><a class="txt" href="topalg_4.html#E2:43_1_1_1"><i><font color="Green" title="E30">A1</font></i></a>, <a class="txt" href="topalg_4.html#E5:43_1_1_1"><i><font color="Green" title="E32">A3</font></i></a>, <a class="ref" href="topalg_1.html#T62" title="TOPALG_1:th.62">TOPALG_1:62</a></i>;<br/><a NAME="E13:43_1_1_1"/><b>then </b><i><font color="Green" title="E36">A7</font></i>: 
<font color="Maroon" title="c13">lab</font>,<font color="Maroon" title="c11">la</font> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Maroon" title="c12">lb</font> <a href="borsuk_2.html#R3" title="BORSUK_2:pred.3">are_homotopic</a> 
 <b>by </b><i><a class="txt" href="topalg_4.html#E8:43_1_1_1"><i><font color="Green" title="E34">A5</font></i></a>, <a class="ref" href="topalg_1.html#T47" title="TOPALG_1:th.47">TOPALG_1:47</a></i>;<br/><a NAME="E14:43_1_1_1"/><b>then </b><i><font color="Green" title="E37">A8</font></i>: 
 <a href="topalg_4.html#K10" title="TOPALG_4:func.10">pr1</a> <font color="Maroon" title="c13">lab</font>, <a href="topalg_4.html#K10" title="TOPALG_4:func.10">pr1</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">la</font> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Maroon" title="c12">lb</font></span>)</span> <a href="borsuk_2.html#R3" title="BORSUK_2:pred.3">are_homotopic</a> 
 <b>by </b><i><a class="ref" href="topalg_4.html#T19" target="_self" title="TOPALG_4:th.19">Th19</a></i>;<br/><a NAME="E15:43_1_1_1"/><i><font color="Green" title="E38">A9</font></i>: 
 <a href="topalg_4.html#K11" title="TOPALG_4:func.11">pr2</a> <font color="Maroon" title="c13">lab</font>, <a href="topalg_4.html#K11" title="TOPALG_4:func.11">pr2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">la</font> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Maroon" title="c12">lb</font></span>)</span> <a href="borsuk_2.html#R3" title="BORSUK_2:pred.3">are_homotopic</a> 
 <b>by </b><i><a class="txt" href="topalg_4.html#E13:43_1_1_1"><i><font color="Green" title="E36">A7</font></i></a>, <a class="ref" href="topalg_4.html#T20" target="_self" title="TOPALG_4:th.20">Th20</a></i>;<br/><i><font color="Green" title="E39">A10</font></i>: <font color="Maroon" title="c14">A1</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c15">A2</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="c4">S</font>,<font color="Maroon" title="c6">s</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="topalg_4.html#K10" title="TOPALG_4:func.10">pr1</a> <font color="Maroon" title="c11">la</font></span>)</span> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <span class="p2">(<span class="default"><a href="topalg_4.html#K10" title="TOPALG_4:func.10">pr1</a> <font color="Maroon" title="c12">lb</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="topalg_1.html#T62" title="TOPALG_1:th.62">TOPALG_1:62</a></i>
<br/>.= 
 <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="c4">S</font>,<font color="Maroon" title="c6">s</font></span>)</span>,<span class="p1">(<span class="default"><a href="topalg_4.html#K10" title="TOPALG_4:func.10">pr1</a> <span class="p2">(<span class="default"><font color="Maroon" title="c11">la</font> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Maroon" title="c12">lb</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="topalg_4.html#T23" target="_self" title="TOPALG_4:th.23">Th23</a></i>
<br/>.= 
 <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="c4">S</font>,<font color="Maroon" title="c6">s</font></span>)</span>,<span class="p1">(<span class="default"><a href="topalg_4.html#K10" title="TOPALG_4:func.10">pr1</a> <font color="Maroon" title="c13">lab</font></span>)</span>
<b>by </b><i><a class="txt" href="topalg_4.html#E14:43_1_1_1"><i><font color="Green" title="E37">A8</font></i></a>, <a class="ref" href="topalg_1.html#T47" title="TOPALG_1:th.47">TOPALG_1:47</a></i>
;<br/><font color="Maroon" title="c16">B1</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c17">B2</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">T</font>,<font color="Maroon" title="c7">t</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="topalg_4.html#K11" title="TOPALG_4:func.11">pr2</a> <font color="Maroon" title="c11">la</font></span>)</span> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <span class="p2">(<span class="default"><a href="topalg_4.html#K11" title="TOPALG_4:func.11">pr2</a> <font color="Maroon" title="c12">lb</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="topalg_1.html#T62" title="TOPALG_1:th.62">TOPALG_1:62</a></i>
<br/>.= 
 <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">T</font>,<font color="Maroon" title="c7">t</font></span>)</span>,<span class="p1">(<span class="default"><a href="topalg_4.html#K11" title="TOPALG_4:func.11">pr2</a> <span class="p2">(<span class="default"><font color="Maroon" title="c11">la</font> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Maroon" title="c12">lb</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="topalg_4.html#T25" target="_self" title="TOPALG_4:th.25">Th25</a></i>
<br/>.= 
 <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">T</font>,<font color="Maroon" title="c7">t</font></span>)</span>,<span class="p1">(<span class="default"><a href="topalg_4.html#K11" title="TOPALG_4:func.11">pr2</a> <font color="Maroon" title="c13">lab</font></span>)</span>
<b>by </b><i><a class="txt" href="topalg_4.html#E15:43_1_1_1"><i><font color="Green" title="E38">A9</font></i></a>, <a class="ref" href="topalg_1.html#T47" title="TOPALG_1:th.47">TOPALG_1:47</a></i>
;<br/><b>hence </b><a NAME="E18:43_1_1_1"/>
<span class="p1">(<span class="default"><a href="topalg_4.html#K12" title="TOPALG_4:func.12">FGPrIso</a> <font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c7">t</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c10">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="topalg_4.html#K12" title="TOPALG_4:func.12">FGPrIso</a> <font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c7">t</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">a</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="topalg_4.html#K12" title="TOPALG_4:func.12">FGPrIso</a> <font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c7">t</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">b</font></span>)</span>
 <b>by </b><i><a class="txt" href="topalg_4.html#E3:43_1_1_1"><i><font color="Green" title="E31">A2</font></i></a>, <a class="txt" href="topalg_4.html#E6:43_1_1_1"><i><font color="Green" title="E33">A4</font></i></a>, <a class="txt" href="topalg_4.html#E9:43_1_1_1"><i><font color="Green" title="E35">A6</font></i></a>, <a class="txt" href="topalg_4.html#E16:43_1_1_1"><i><font color="Green" title="E39">A10</font></i></a>, <a class="ref" href="group_7.html#T32" title="GROUP_7:th.32">GROUP_7:32</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:43_1_1"/>
 <a href="topalg_4.html#K12" title="TOPALG_4:func.12">FGPrIso</a> <font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c7">t</font> is   <a href="group_6.html#NM2" title="GROUP_6:NM.2">Homomorphism</a> of <span class="p1">(<span class="default"><a href="topalg_1.html#NK4" title="TOPALG_1:NK.4">pi_1</a> <span class="p2"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c5">T</font></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span>,<span class="p2"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c7">t</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span>,<span class="p1">(<span class="default"><a href="group_7.html#K2" title="GROUP_7:func.2">product</a> <span class="p2"><a href="group_7.html#K15" title="GROUP_7:func.15">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="topalg_1.html#NK4" title="TOPALG_1:NK.4">pi_1</a> <font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c6">s</font></span>)</span>,<span class="p3">(<span class="default"><a href="topalg_1.html#NK4" title="TOPALG_1:NK.4">pi_1</a> <font color="Maroon" title="c5">T</font>,<font color="Maroon" title="c7">t</font></span>)</span></span><a href="group_7.html#K15" title="GROUP_7:func.15">*&gt;</a></span></span>)</span>
 <b>by </b><i><a class="ref" href="group_6.html#D7" title="GROUP_6:def.7">GROUP_6:def 7</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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