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<span class="kw">let </span><font color="Maroon" title="c4">S</font>, <font color="Maroon" title="c5">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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">s</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c4">S</font><br/> for <font color="Olive" title="b2">f</font> being  <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="c4">S</font>,<font color="Maroon" title="c5">T</font>  st <font color="Olive" title="b2">f</font> is  <a href="tops_2.html#V3" title="TOPS_2:attr.3">being_homeomorphism</a>  holds <br/> <a href="topalg_3.html#K4" title="TOPALG_3:func.4">FundGrIso</a> <font color="Olive" title="b2">f</font>,<font color="Olive" title="b1">s</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c6">s</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c4">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">f</font> being  <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="c4">S</font>,<font color="Maroon" title="c5">T</font>  st <font color="Olive" title="b1">f</font> is  <a href="tops_2.html#V3" title="TOPS_2:attr.3">being_homeomorphism</a>  holds <br/> <a href="topalg_3.html#K4" title="TOPALG_3:func.4">FundGrIso</a> <font color="Olive" title="b1">f</font>,<font color="Maroon" title="c6">s</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a> </span><br/>



<span class="kw">set </span><font color="Maroon" title="c7">pS</font> =  <a href="topalg_1.html#NK6" title="TOPALG_1:NK.6">pi_1</a> <font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c6">s</font>;<br/>
<span class="kw">let </span><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="c4">S</font>,<font color="Maroon" title="c5">T</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c8">f</font> is  <a href="tops_2.html#V3" title="TOPS_2:attr.3">being_homeomorphism</a>  implies  <a href="topalg_3.html#K4" title="TOPALG_3:func.4">FundGrIso</a> <font color="Maroon" title="c8">f</font>,<font color="Maroon" title="c6">s</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:42"/><span class="lab"><font color="Green" title="E16">A1</font></span>: 
<font color="Maroon" title="c8">f</font> is  <a href="tops_2.html#V3" title="TOPS_2:attr.3">being_homeomorphism</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="topalg_3.html#K4" title="TOPALG_3:func.4">FundGrIso</a> <font color="Maroon" title="c8">f</font>,<font color="Maroon" title="c6">s</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a> </span><br/>

<a NAME="E2:42"/><span class="lab"><font color="Green" title="E17">A2</font></span>: 
<font color="Maroon" title="c8">f</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42"><span class="lab"><font color="Green" title="E16">A1</font></span></a>, <a class="ref" href="tops_2.html#D5" title="TOPS_2:def.5">TOPS_2:def 5</a></span>;<br/>
<a NAME="E3:42"/><span class="kw">then </span><span class="lab"><font color="Green" title="E18">A3</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">f</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<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="c6">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">s</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T32" title="FUNCT_2:th.32">FUNCT_2:32</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">h</font> =  <a href="topalg_3.html#K4" title="TOPALG_3:func.4">FundGrIso</a> <font color="Maroon" title="c8">f</font>,<font color="Maroon" title="c6">s</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">pT</font> =  <a href="topalg_1.html#NK6" title="TOPALG_1:NK.6">pi_1</a> <font color="Maroon" title="c5">T</font>,<span class="p1">(<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="c6">s</font></span>)</span>;<br/>
<a NAME="E4:42"/><span class="lab"><font color="Green" title="E19">A4</font></span>: 
<font color="Maroon" title="c8">f</font> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a>  is  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42"><span class="lab"><font color="Green" title="E16">A1</font></span></a>, <a class="ref" href="tops_2.html#D5" title="TOPS_2:def.5">TOPS_2:def 5</a></span>;<br/>
<a NAME="E5:42"/><span class="lab"><font color="Green" title="E20">A5</font></span>: 
 <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c8">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c5">T</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42"><span class="lab"><font color="Green" title="E16">A1</font></span></a>, <a class="ref" href="tops_2.html#D5" title="TOPS_2:def.5">TOPS_2:def 5</a></span>;<br/>
<a NAME="E6:42"/><span class="kw">then </span><span class="lab"><font color="Green" title="E21">A6</font></span>: 
<font color="Maroon" title="c8">f</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">f</font> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:42"><span class="lab"><font color="Green" title="E17">A2</font></span></a>, <a class="ref" href="tops_2.html#D4" title="TOPS_2:def.4">TOPS_2:def 4</a></span>;<br/>
<a NAME="E7:42"/><span class="lab"><font color="Green" title="E22">A7</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="topalg_3.html#K4" title="TOPALG_3:func.4">FundGrIso</a> <font color="Maroon" title="c8">f</font>,<font color="Maroon" title="c6">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="topalg_1.html#NK6" title="TOPALG_1:NK.6">pi_1</a> <font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c6">s</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E8:42"/><span class="lab"><font color="Green" title="E23">A8</font></span>: 
 <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="topalg_3.html#K4" title="TOPALG_3:func.4">FundGrIso</a> <font color="Maroon" title="c8">f</font>,<font color="Maroon" title="c6">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="topalg_1.html#NK6" title="TOPALG_1:NK.6">pi_1</a> <font color="Maroon" title="c5">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="c6">s</font></span>)</span></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="42_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">thus </span><a NAME="E1:42_1"/>
 <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="topalg_3.html#K4" title="TOPALG_3:func.4">FundGrIso</a> <font color="Maroon" title="c8">f</font>,<font color="Maroon" title="c6">s</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="topalg_1.html#NK6" title="TOPALG_1:NK.6">pi_1</a> <font color="Maroon" title="c5">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="c6">s</font></span>)</span></span>)</span>
 ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="topalg_1.html#NK6" title="TOPALG_1:NK.6">pi_1</a> <font color="Maroon" title="c5">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="c6">s</font></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="topalg_3.html#K4" title="TOPALG_3:func.4">FundGrIso</a> <font color="Maroon" title="c8">f</font>,<font color="Maroon" title="c6">s</font></span>)</span></span><br/>

<span class="kw">let </span><font color="Maroon" title="c11">y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c11">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="topalg_1.html#NK6" title="TOPALG_1:NK.6">pi_1</a> <font color="Maroon" title="c5">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="c6">s</font></span>)</span></span>)</span> or <font color="Maroon" title="c11">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="topalg_3.html#K4" title="TOPALG_3:func.4">FundGrIso</a> <font color="Maroon" title="c8">f</font>,<font color="Maroon" title="c6">s</font></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E2:42_1"/>
<font color="Maroon" title="c11">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="topalg_1.html#NK6" title="TOPALG_1:NK.6">pi_1</a> <font color="Maroon" title="c5">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="c6">s</font></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c11">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="topalg_3.html#K4" title="TOPALG_3:func.4">FundGrIso</a> <font color="Maroon" title="c8">f</font>,<font color="Maroon" title="c6">s</font></span>)</span></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c12">lt</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="c6">s</font><span class="kw"> such that </span><br/><a NAME="E4:42_1"/><span class="lab"><font color="Green" title="E24">A9</font></span>: 
<font color="Maroon" title="c11">y</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#K4" title="TOPALG_1:func.4">EqRel</a> <font color="Maroon" title="c5">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="c6">s</font></span>)</span></span>)</span>,<font color="Maroon" title="c12">lt</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="topalg_1.html#T48" title="TOPALG_1:th.48">TOPALG_1:48</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c13">ls</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c8">f</font> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a> </span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c12">lt</font> as   <a href="topalg_1.html#NM1" title="TOPALG_1:NM.1">Loop</a> of <font color="Maroon" title="c6">s</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:42"><span class="lab"><font color="Green" title="E19">A4</font></span></a>, <a class="txt" href="#E3:42"><span class="lab"><font color="Green" title="E18">A3</font></span></a>, <a class="txt" href="#E6:42"><span class="lab"><font color="Green" title="E21">A6</font></span></a>, <a class="ref" href="topalg_3.html#T27" target="_self" title="TOPALG_3:th.27">Th27</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c14">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#K4" title="TOPALG_1:func.4">EqRel</a> <font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c6">s</font></span>)</span>,<font color="Maroon" title="c13">ls</font>;<br/>
<a NAME="E6:42_1"/><span class="lab"><font color="Green" title="E25">A10</font></span>: 
 <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <span class="p1">(<span class="default"><a href="topalg_1.html#K4" title="TOPALG_1:func.4">EqRel</a> <font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c6">s</font></span>)</span>,<font color="Maroon" title="c13">ls</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="topalg_1.html#NK6" title="TOPALG_1:NK.6">pi_1</a> <font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c6">s</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="topalg_1.html#T48" title="TOPALG_1:th.48">TOPALG_1:48</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c15">ls1</font> being   <a href="topalg_1.html#NM1" title="TOPALG_1:NM.1">Loop</a> of <font color="Maroon" title="c6">s</font><span class="kw"> such that </span><br/><a NAME="E8:42_1"/><span class="lab"><font color="Green" title="E26">A11</font></span>: 
 <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <span class="p1">(<span class="default"><a href="topalg_1.html#K4" title="TOPALG_1:func.4">EqRel</a> <font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c6">s</font></span>)</span>,<font color="Maroon" title="c13">ls</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#K4" title="TOPALG_1:func.4">EqRel</a> <font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c6">s</font></span>)</span>,<font color="Maroon" title="c15">ls1</font>
 <span class="kw">and </span><br/><a NAME="E9:42_1"/><span class="lab"><font color="Green" title="E27">A12</font></span>: 
<span class="p1">(<span class="default"><a href="topalg_3.html#K4" title="TOPALG_3:func.4">FundGrIso</a> <font color="Maroon" title="c8">f</font>,<font color="Maroon" title="c6">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#K4" title="TOPALG_1:func.4">EqRel</a> <font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c6">s</font></span>)</span>,<font color="Maroon" title="c13">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#K4" title="TOPALG_1:func.4">EqRel</a> <font color="Maroon" title="c5">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="c6">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="c15">ls1</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="topalg_3.html#D1" target="_self" title="TOPALG_3:def.1">Def1</a></span>;<br/>
<span class="lab"><font color="Green" title="E28">A13</font></span>: <font color="Maroon" title="c8">f</font> <a href="topalg_3.html#K2" title="TOPALG_3:func.2">*</a> <font color="Maroon" title="c13">ls</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">f</font> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a> </span>)</span></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c12">lt</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T55" title="RELAT_1:th.55">RELAT_1:55</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p2">(<span class="default"><a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c8">f</font></span>)</span></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c12">lt</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:42"><span class="lab"><font color="Green" title="E20">A5</font></span></a>, <a class="txt" href="#E2:42"><span class="lab"><font color="Green" title="E17">A2</font></span></a>, <a class="ref" href="tops_2.html#T65" title="TOPS_2:th.65">TOPS_2:65</a></span>
<br/>.= 
<font color="Maroon" title="c12">lt</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:42"><span class="lab"><font color="Green" title="E20">A5</font></span></a>, <a class="ref" href="funct_2.html#T23" title="FUNCT_2:th.23">FUNCT_2:23</a></span>
;<br/>
<a NAME="E11:42_1"/>
<font color="Maroon" title="c13">ls</font>,<font color="Maroon" title="c15">ls1</font> <a href="borsuk_2.html#R3" title="BORSUK_2:pred.3">are_homotopic</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:42_1"><span class="lab"><font color="Green" title="E26">A11</font></span></a>, <a class="ref" href="topalg_1.html#T47" title="TOPALG_1:th.47">TOPALG_1:47</a></span>;<br/>
<a NAME="E12:42_1"/><span class="kw">then </span>
<font color="Maroon" title="c12">lt</font>,<font color="Maroon" title="c8">f</font> <a href="topalg_3.html#K2" title="TOPALG_3:func.2">*</a> <font color="Maroon" title="c15">ls1</font> <a href="borsuk_2.html#R3" title="BORSUK_2:pred.3">are_homotopic</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:42_1"><span class="lab"><font color="Green" title="E28">A13</font></span></a>, <a class="ref" href="topalg_3.html#T28" target="_self" title="TOPALG_3:th.28">Th28</a></span>;<br/>
<a NAME="E13:42_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="topalg_3.html#K4" title="TOPALG_3:func.4">FundGrIso</a> <font color="Maroon" title="c8">f</font>,<font color="Maroon" title="c6">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#K4" title="TOPALG_1:func.4">EqRel</a> <font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c6">s</font></span>)</span>,<font color="Maroon" title="c13">ls</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:42_1"><span class="lab"><font color="Green" title="E24">A9</font></span></a>, <a class="txt" href="#E9:42_1"><span class="lab"><font color="Green" title="E27">A12</font></span></a>, <a class="ref" href="topalg_1.html#T47" title="TOPALG_1:th.47">TOPALG_1:47</a></span>;<br/>
<span class="kw">hence </span><a NAME="E14:42_1"/>
<font color="Maroon" title="c11">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="topalg_3.html#K4" title="TOPALG_3:func.4">FundGrIso</a> <font color="Maroon" title="c8">f</font>,<font color="Maroon" title="c6">s</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:42"><span class="lab"><font color="Green" title="E22">A7</font></span></a>, <a class="txt" href="#E6:42_1"><span class="lab"><font color="Green" title="E25">A10</font></span></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E9:42"/><span class="lab"><font color="Green" title="E24">A14</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c8">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c4">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42"><span class="lab"><font color="Green" title="E16">A1</font></span></a>, <a class="ref" href="tops_2.html#D5" title="TOPS_2:def.5">TOPS_2:def 5</a></span>;<br/>
<a NAME="E10:42"/>
 <a href="topalg_3.html#K4" title="TOPALG_3:func.4">FundGrIso</a> <font color="Maroon" title="c8">f</font>,<font color="Maroon" title="c6">s</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="42_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c11">x1</font>, <font color="Maroon" title="c12">x2</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="funct_1.html#D8" title="FUNCT_1:def.8">FUNCT_1:def 8</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c11">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <span class="p1">(<span class="default"><a href="topalg_3.html#K4" title="TOPALG_3:func.4">FundGrIso</a> <font color="Maroon" title="c8">f</font>,<font color="Maroon" title="c6">s</font></span>)</span> or  not <font color="Maroon" title="c12">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <span class="p1">(<span class="default"><a href="topalg_3.html#K4" title="TOPALG_3:func.4">FundGrIso</a> <font color="Maroon" title="c8">f</font>,<font color="Maroon" title="c6">s</font></span>)</span> or  not <span class="p1">(<span class="default"><a href="topalg_3.html#K4" title="TOPALG_3:func.4">FundGrIso</a> <font color="Maroon" title="c8">f</font>,<font color="Maroon" title="c6">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="topalg_3.html#K4" title="TOPALG_3:func.4">FundGrIso</a> <font color="Maroon" title="c8">f</font>,<font color="Maroon" title="c6">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">x2</font> or <font color="Maroon" title="c11">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">x2</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:42_2"/>
<font color="Maroon" title="c11">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="topalg_3.html#K4" title="TOPALG_3:func.4">FundGrIso</a> <font color="Maroon" title="c8">f</font>,<font color="Maroon" title="c6">s</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c12">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <span class="p1">(<span class="default"><a href="topalg_3.html#K4" title="TOPALG_3:func.4">FundGrIso</a> <font color="Maroon" title="c8">f</font>,<font color="Maroon" title="c6">s</font></span>)</span> or  not <span class="p1">(<span class="default"><a href="topalg_3.html#K4" title="TOPALG_3:func.4">FundGrIso</a> <font color="Maroon" title="c8">f</font>,<font color="Maroon" title="c6">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="topalg_3.html#K4" title="TOPALG_3:func.4">FundGrIso</a> <font color="Maroon" title="c8">f</font>,<font color="Maroon" title="c6">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">x2</font> or <font color="Maroon" title="c11">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">x2</font> )</span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c13">ls1</font> being   <a href="topalg_1.html#NM1" title="TOPALG_1:NM.1">Loop</a> of <font color="Maroon" title="c6">s</font><span class="kw"> such that </span><br/><a NAME="E3:42_2"/><span class="lab"><font color="Green" title="E25">A15</font></span>: 
<font color="Maroon" title="c11">x1</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#K4" title="TOPALG_1:func.4">EqRel</a> <font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c6">s</font></span>)</span>,<font color="Maroon" title="c13">ls1</font>
 <span class="kw">and </span><br/><a NAME="E4:42_2"/><span class="lab"><font color="Green" title="E26">A16</font></span>: 
<span class="p1">(<span class="default"><a href="topalg_3.html#K4" title="TOPALG_3:func.4">FundGrIso</a> <font color="Maroon" title="c8">f</font>,<font color="Maroon" title="c6">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x1</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#K4" title="TOPALG_1:func.4">EqRel</a> <font color="Maroon" title="c5">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="c6">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="c13">ls1</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="topalg_3.html#D1" target="_self" title="TOPALG_3:def.1">Def1</a></span>;<br/>
<span class="kw">assume </span><a NAME="E5:42_2"/>
<font color="Maroon" title="c12">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="topalg_3.html#K4" title="TOPALG_3:func.4">FundGrIso</a> <font color="Maroon" title="c8">f</font>,<font color="Maroon" title="c6">s</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <span class="p1">(<span class="default"><a href="topalg_3.html#K4" title="TOPALG_3:func.4">FundGrIso</a> <font color="Maroon" title="c8">f</font>,<font color="Maroon" title="c6">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="topalg_3.html#K4" title="TOPALG_3:func.4">FundGrIso</a> <font color="Maroon" title="c8">f</font>,<font color="Maroon" title="c6">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">x2</font> or <font color="Maroon" title="c11">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">x2</font> )</span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c14">ls2</font> being   <a href="topalg_1.html#NM1" title="TOPALG_1:NM.1">Loop</a> of <font color="Maroon" title="c6">s</font><span class="kw"> such that </span><br/><a NAME="E7:42_2"/><span class="lab"><font color="Green" title="E27">A17</font></span>: 
<font color="Maroon" title="c12">x2</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#K4" title="TOPALG_1:func.4">EqRel</a> <font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c6">s</font></span>)</span>,<font color="Maroon" title="c14">ls2</font>
 <span class="kw">and </span><br/><a NAME="E8:42_2"/><span class="lab"><font color="Green" title="E28">A18</font></span>: 
<span class="p1">(<span class="default"><a href="topalg_3.html#K4" title="TOPALG_3:func.4">FundGrIso</a> <font color="Maroon" title="c8">f</font>,<font color="Maroon" title="c6">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">x2</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#K4" title="TOPALG_1:func.4">EqRel</a> <font color="Maroon" title="c5">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="c6">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="c14">ls2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="topalg_3.html#D1" target="_self" title="TOPALG_3:def.1">Def1</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c15">a1</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c8">f</font> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a> </span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <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="c13">ls1</font></span>)</span>, <font color="Maroon" title="c16">a2</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c8">f</font> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a> </span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <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="c14">ls2</font></span>)</span> as   <a href="topalg_1.html#NM1" title="TOPALG_1:NM.1">Loop</a> of <font color="Maroon" title="c6">s</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:42"><span class="lab"><font color="Green" title="E19">A4</font></span></a>, <a class="txt" href="#E3:42"><span class="lab"><font color="Green" title="E18">A3</font></span></a>, <a class="txt" href="#E6:42"><span class="lab"><font color="Green" title="E21">A6</font></span></a>, <a class="ref" href="topalg_3.html#T27" target="_self" title="TOPALG_3:th.27">Th27</a></span>;<br/>
<span class="kw">assume </span><a NAME="E10:42_2"/>
<span class="p1">(<span class="default"><a href="topalg_3.html#K4" title="TOPALG_3:func.4">FundGrIso</a> <font color="Maroon" title="c8">f</font>,<font color="Maroon" title="c6">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="topalg_3.html#K4" title="TOPALG_3:func.4">FundGrIso</a> <font color="Maroon" title="c8">f</font>,<font color="Maroon" title="c6">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">x2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c11">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">x2</font></span><br/>

<a NAME="E11:42_2"/><span class="kw">then </span>
<font color="Maroon" title="c8">f</font> <a href="topalg_3.html#K2" title="TOPALG_3:func.2">*</a> <font color="Maroon" title="c13">ls1</font>,<font color="Maroon" title="c8">f</font> <a href="topalg_3.html#K2" title="TOPALG_3:func.2">*</a> <font color="Maroon" title="c14">ls2</font> <a href="borsuk_2.html#R3" title="BORSUK_2:pred.3">are_homotopic</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:42_2"><span class="lab"><font color="Green" title="E26">A16</font></span></a>, <a class="txt" href="#E8:42_2"><span class="lab"><font color="Green" title="E28">A18</font></span></a>, <a class="ref" href="topalg_1.html#T47" title="TOPALG_1:th.47">TOPALG_1:47</a></span>;<br/>
<a NAME="E12:42_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E29">A19</font></span>: 
<font color="Maroon" title="c15">a1</font>,<font color="Maroon" title="c16">a2</font> <a href="borsuk_2.html#R3" title="BORSUK_2:pred.3">are_homotopic</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:42"><span class="lab"><font color="Green" title="E19">A4</font></span></a>, <a class="txt" href="#E3:42"><span class="lab"><font color="Green" title="E18">A3</font></span></a>, <a class="txt" href="#E6:42"><span class="lab"><font color="Green" title="E21">A6</font></span></a>, <a class="ref" href="topalg_3.html#T28" target="_self" title="TOPALG_3:th.28">Th28</a></span>;<br/>
<a NAME="E13:42_2"/><span class="lab"><font color="Green" title="E30">A20</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">f</font> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a> </span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c8">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c8">f</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:42"><span class="lab"><font color="Green" title="E20">A5</font></span></a>, <a class="txt" href="#E2:42"><span class="lab"><font color="Green" title="E17">A2</font></span></a>, <a class="ref" href="tops_2.html#T65" title="TOPS_2:th.65">TOPS_2:65</a></span>;<br/>
<span class="lab"><font color="Green" title="E31">A21</font></span>: <span class="p1">(<span class="default"><font color="Maroon" title="c8">f</font> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a> </span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <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="c13">ls1</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">f</font> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a> </span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c8">f</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c13">ls1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T55" title="RELAT_1:th.55">RELAT_1:55</a></span>
<br/>.= 
<font color="Maroon" title="c13">ls1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:42"><span class="lab"><font color="Green" title="E24">A14</font></span></a>, <a class="txt" href="#E13:42_2"><span class="lab"><font color="Green" title="E30">A20</font></span></a>, <a class="ref" href="funct_2.html#T23" title="FUNCT_2:th.23">FUNCT_2:23</a></span>
;<br/>
<span class="p1">(<span class="default"><font color="Maroon" title="c8">f</font> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a> </span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <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="c14">ls2</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">f</font> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a> </span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c8">f</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c14">ls2</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T55" title="RELAT_1:th.55">RELAT_1:55</a></span>
<br/>.= 
<font color="Maroon" title="c14">ls2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:42"><span class="lab"><font color="Green" title="E24">A14</font></span></a>, <a class="txt" href="#E13:42_2"><span class="lab"><font color="Green" title="E30">A20</font></span></a>, <a class="ref" href="funct_2.html#T23" title="FUNCT_2:th.23">FUNCT_2:23</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E16:42_2"/>
<font color="Maroon" title="c11">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">x2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:42_2"><span class="lab"><font color="Green" title="E25">A15</font></span></a>, <a class="txt" href="#E7:42_2"><span class="lab"><font color="Green" title="E27">A17</font></span></a>, <a class="txt" href="#E14:42_2"><span class="lab"><font color="Green" title="E31">A21</font></span></a>, <a class="txt" href="#E12:42_2"><span class="lab"><font color="Green" title="E29">A19</font></span></a>, <a class="ref" href="topalg_1.html#T47" title="TOPALG_1:th.47">TOPALG_1:47</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E11:42"/>
 <a href="topalg_3.html#K4" title="TOPALG_3:func.4">FundGrIso</a> <font color="Maroon" title="c8">f</font>,<font color="Maroon" title="c6">s</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:42"><span class="lab"><font color="Green" title="E23">A8</font></span></a>, <a class="ref" href="group_6.html#T70" title="GROUP_6:th.70">GROUP_6:70</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
