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

<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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">t</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c5">T</font><br/> for <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="Olive" title="b1">s</font>,<font color="Olive" title="b2">t</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> holds  <span class="p1">(<span class="default"><a href="topalg_4.html#K12" title="TOPALG_4:func.12">FGPrIso</a> <font color="Olive" title="b1">s</font>,<font color="Olive" title="b2">t</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#K2" title="TOPALG_1:func.2">EqRel</a> <span class="p3"><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="p3"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Olive" title="b1">s</font>,<font color="Olive" title="b2">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></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="Olive" title="b1">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="Olive" title="b2">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></span><br/><b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">t</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c5">T</font><br/> for <font color="Olive" title="b2">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="Olive" title="b1">t</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> holds  <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="Olive" title="b1">t</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#K2" title="TOPALG_1:func.2">EqRel</a> <span class="p3"><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="p3"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c6">s</font>,<font color="Olive" title="b1">t</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span></span>)</span>,<font color="Olive" title="b2">l</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="Olive" title="b2">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="Olive" title="b1">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="b2">l</font></span>)</span></span>)</span></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></span><br/><b>let </b><font color="Maroon" title="c7">t</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c5">T</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <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> holds  <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_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#K2" title="TOPALG_1:func.2">EqRel</a> <span class="p3"><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="p3"><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></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="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></span><br/><b>let </b><font color="Maroon" title="c8">l</font> be   <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>; <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_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#K2" title="TOPALG_1:func.2">EqRel</a> <span class="p3"><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="p3"><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="c8">l</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="c8">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="c8">l</font></span>)</span></span>)</span></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></span><br/>









<a NAME="E1:41"/>
 <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="c8">l</font> is   <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>
 
<b>by </b><i><a class="ref" href="topalg_1.html#T48" title="TOPALG_1:th.48">TOPALG_1:48</a></i>;<br/>
<b>hence </b><a NAME="E2:41"/>
<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_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#K2" title="TOPALG_1:func.2">EqRel</a> <span class="p3"><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="p3"><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="c8">l</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="c8">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="c8">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="ref" href="topalg_4.html#T27" target="_self" title="TOPALG_4:th.27">Th27</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>
