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<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ,   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ] <b>means </b> ex <font color="Olive" title="b1">l</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> st <br/>( $1 <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="Olive" title="b1">l</font> &amp; $2 <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="Olive" title="b1">l</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="Olive" title="b1">l</font></span>)</span></span>)</span></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> );<br/>
<a NAME="E1:39_1_1"/><i><font color="Green" title="E27">A1</font></i>: 
for <font color="Olive" title="b1">x</font> being  <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>  ex <font color="Olive" title="b2">y</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <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> st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c11">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="topalg_1.html#NK4" title="TOPALG_1:NK.4">pi_1</a> <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">  ex <font color="Olive" title="b1">y</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <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> st <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c11">x</font>,<font color="Olive" title="b1">y</font>]</span><br/>

<b>consider </b><font color="Maroon" title="c12">l</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="E2:39_1_1_1"/><i><font color="Green" title="E28">A2</font></i>: 
<font color="Maroon" title="c11">x</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">l</font>
 <b>by </b><i><a class="ref" href="topalg_1.html#T48" title="TOPALG_1:th.48">TOPALG_1:48</a></i>;<br/>
<b>set </b><font color="Maroon" title="c13">A</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">l</font></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c14">B</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">l</font></span>)</span>;<br/>
<a NAME="E3:39_1_1_1"/><i><font color="Green" title="E29">A3</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><a href="pralg_1.html#K12" title="PRALG_1:func.12">Carrier</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_7.html#D2" title="GROUP_7:def.2">GROUP_7:def 2</a></i>;<br/>
<a NAME="E4:39_1_1_1"/><i><font color="Green" title="E30">A4</font></i>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</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">l</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">l</font></span>)</span></span>)</span></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">1,2</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T4" title="FINSEQ_1:th.4">FINSEQ_1:4</a>, <a class="ref" href="finseq_3.html#T29" title="FINSEQ_3:th.29">FINSEQ_3:29</a></i>;<br/>
<a NAME="E5:39_1_1_1"/><i><font color="Green" title="E31">A5</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="pralg_1.html#K12" title="PRALG_1:func.12">Carrier</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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">1,2</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
<b>by </b><i><a class="ref" href="pboole.html#D3" title="PBOOLE:def.3">PBOOLE:def 3</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_1_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c15">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c15">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="pralg_1.html#K12" title="PRALG_1:func.12">Carrier</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> implies <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">l</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">l</font></span>)</span></span>)</span></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="pralg_1.html#K12" title="PRALG_1:func.12">Carrier</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> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">x</font> )</span><br/><b>assume </b><a NAME="E1:39_1_1_1_1"/><i><font color="Green" title="E32">A6</font></i>: 
<font color="Maroon" title="c15">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="pralg_1.html#K12" title="PRALG_1:func.12">Carrier</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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <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">l</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">l</font></span>)</span></span>)</span></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="pralg_1.html#K12" title="PRALG_1:func.12">Carrier</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> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">x</font></span><br/><a NAME="E2:39_1_1_1_1"/><i><font color="Green" title="E33">A7</font></i>: 
 ex <font color="Olive" title="b1">R</font> being   <a href="struct_0.html#L1" title="STRUCT_0:struct.1">1-sorted</a>  st <br/>( <font color="Olive" title="b1">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="group_7.html#K15" title="GROUP_7:func.15">&lt;*</a><span class="default"><span class="p2">(<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="p2">(<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> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">x</font> &amp; <span class="p1">(<span class="default"><a href="pralg_1.html#K12" title="PRALG_1:func.12">Carrier</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> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">x</font> <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 <font color="Olive" title="b1">R</font> )
 <b>by </b><i><a class="txt" href="topalg_4.html#E5:39_1_1_1"><i><font color="Green" title="E31">A5</font></i></a>, <a class="txt" href="topalg_4.html#E1:39_1_1_1_1"><i><font color="Green" title="E32">A6</font></i></a>, <a class="ref" href="pralg_1.html#D13" title="PRALG_1:def.13">PRALG_1:def 13</a></i>;<br/><a NAME="E3:39_1_1_1_1"/><i><font color="Green" title="E34">A8</font></i>: 
( <span class="p1"><a href="group_7.html#K15" title="GROUP_7:func.15">&lt;*</a><span class="default"><span class="p2">(<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="p2">(<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> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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> &amp; <span class="p1"><a href="group_7.html#K15" title="GROUP_7:func.15">&lt;*</a><span class="default"><span class="p2">(<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="p2">(<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> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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> )
 <b>by </b><i><a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></i>;<br/><a NAME="E4:39_1_1_1_1"/><i><font color="Green" title="E35">A9</font></i>: 
( <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">l</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">l</font></span>)</span></span>)</span></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <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> <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">l</font></span>)</span> &amp; <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">l</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">l</font></span>)</span></span>)</span></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <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> <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">l</font></span>)</span> )
 <b>by </b><i><a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></i>;<br/><a NAME="E5:39_1_1_1_1"/>
( <font color="Maroon" title="c15">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or <font color="Maroon" title="c15">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 )
 <b>by </b><i><a class="txt" href="topalg_4.html#E5:39_1_1_1"><i><font color="Green" title="E31">A5</font></i></a>, <a class="txt" href="topalg_4.html#E1:39_1_1_1_1"><i><font color="Green" title="E32">A6</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><b>hence </b><a NAME="E6:39_1_1_1_1"/>
<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">l</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">l</font></span>)</span></span>)</span></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="pralg_1.html#K12" title="PRALG_1:func.12">Carrier</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> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">x</font>
 <b>by </b><i><a class="txt" href="topalg_4.html#E2:39_1_1_1_1"><i><font color="Green" title="E33">A7</font></i></a>, <a class="txt" href="topalg_4.html#E3:39_1_1_1_1"><i><font color="Green" title="E34">A8</font></i></a>, <a class="txt" href="topalg_4.html#E4:39_1_1_1_1"><i><font color="Green" title="E35">A9</font></i></a>, <a class="ref" href="topalg_1.html#T48" title="TOPALG_1:th.48">TOPALG_1:48</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>then reconsider </b><font color="Maroon" title="c15">y</font> = <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">l</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">l</font></span>)</span></span>)</span></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <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="txt" href="topalg_4.html#E3:39_1_1_1"><i><font color="Green" title="E29">A3</font></i></a>, <a class="txt" href="topalg_4.html#E4:39_1_1_1"><i><font color="Green" title="E30">A4</font></i></a>, <a class="txt" href="topalg_4.html#E5:39_1_1_1"><i><font color="Green" title="E31">A5</font></i></a>, <a class="ref" href="card_3.html#T18" title="CARD_3:th.18">CARD_3:18</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c15">y</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c15">y</font>]</span><br/>

<b>take </b>
<font color="Maroon" title="c12">l</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c11">x</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">l</font> &amp; <font color="Maroon" title="c15">y</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">l</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">l</font></span>)</span></span>)</span></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> )</span><br/>

<b>thus </b><a NAME="E8:39_1_1_1"/>
( <font color="Maroon" title="c11">x</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">l</font> &amp; <font color="Maroon" title="c15">y</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">l</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">l</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="txt" href="topalg_4.html#E2:39_1_1_1"><i><font color="Green" title="E28">A2</font></i></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>
<a NAME="E2:39_1_1"/>
 ex <font color="Olive" title="b1">h</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</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> st <br/>for <font color="Olive" title="b2">x</font> being  <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> holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b2">x</font>,<font color="Olive" title="b1">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">x</font>]
 
<b>from </b><i><a class="ref" href="funct_2.html#S3" title="FUNCT_2:sch.3">FUNCT_2:sch 3</a>(<a class="txt" href="topalg_4.html#E1:39_1_1"><i><font color="Green" title="E27">A1</font></i></a>);<br/></i>
<b>hence </b><a NAME="E3:39_1_1"/>
 ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</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> st <br/>for <font color="Olive" title="b2">x</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</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>  ex <font color="Olive" title="b3">l</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> st <br/>( <font color="Olive" title="b2">x</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="Olive" title="b3">l</font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">x</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="Olive" title="b3">l</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="Olive" title="b3">l</font></span>)</span></span>)</span></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
