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

<b>let </b><font color="Maroon" title="c1">X</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">a</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">X</font>;<br/><b>let </b><font color="Maroon" title="c3">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>





<a NAME="E1:57"/><i><font color="Green" title="E36">A1</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="topalg_1.html#NK4" title="TOPALG_1:NK.4">pi_1</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K9" title="EQREL_1:func.9">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="c1">X</font>,<font color="Maroon" title="c2">a</font></span>)</span>
 
<b>by </b><i><a class="ref" href="topalg_1.html#D3" target="_self" title="TOPALG_1:def.3">Def3</a></i>;<br/>
<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:57_1"/>
<font color="Maroon" title="c3">x</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#NK4" title="TOPALG_1:NK.4">pi_1</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">a</font></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon" title="c4">P</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="topalg_1.html#K1" title="TOPALG_1:func.1">Loops</a> <font color="Maroon" title="c2">a</font><b> such that </b><br/><a NAME="E3:57_1"/><i><font color="Green" title="E37">A2</font></i>: 
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K7" title="EQREL_1:func.7">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="c1">X</font>,<font color="Maroon" title="c2">a</font></span>)</span>,<font color="Maroon" title="c4">P</font>
 <b>by </b><i><a class="txt" href="topalg_1.html#E1:57"><i><font color="Green" title="E36">A1</font></i></a>, <a class="ref" href="eqrel_1.html#T45" title="EQREL_1:th.45">EQREL_1:45</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c5">P</font> = <font color="Maroon" title="c4">P</font> as   <a href="topalg_1.html#NM1" title="TOPALG_1:NM.1">Loop</a> of <font color="Maroon" title="c2">a</font> <b>by </b><i><a class="ref" href="topalg_1.html#D1" target="_self" title="TOPALG_1:def.1">Def1</a></i>;<br/><b>take </b><font color="Maroon" title="c6">P</font> = <font color="Maroon" title="c5">P</font>;<br/><b>thus </b><a NAME="E5:57_1"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K7" title="EQREL_1:func.7">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="c1">X</font>,<font color="Maroon" title="c2">a</font></span>)</span>,<font color="Maroon" title="c6">P</font>
 <b>by </b><i><a class="txt" href="topalg_1.html#E3:57_1"><i><font color="Green" title="E37">A2</font></i></a></i>;<br/></div>
<b>end;</b></div>

<b>given </b><font color="Maroon" title="c4">P</font> being   <a href="topalg_1.html#NM1" title="TOPALG_1:NM.1">Loop</a> of <font color="Maroon" title="c2">a</font><b> such that </b><a NAME="E3:57"/><i><font color="Green" title="E37">A3</font></i>: 
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K7" title="EQREL_1:func.7">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="c1">X</font>,<font color="Maroon" title="c2">a</font></span>)</span>,<font color="Maroon" title="c4">P</font>
 ;<br/>

<a NAME="E4:57"/>
<font color="Maroon" title="c4">P</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topalg_1.html#K1" title="TOPALG_1:func.1">Loops</a> <font color="Maroon" title="c2">a</font>
 
<b>by </b><i><a class="ref" href="topalg_1.html#D1" target="_self" title="TOPALG_1:def.1">Def1</a></i>;<br/>
<b>hence </b><a NAME="E5:57"/>
<font color="Maroon" title="c3">x</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#NK4" title="TOPALG_1:NK.4">pi_1</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">a</font></span>)</span>
 <b>by </b><i><a class="txt" href="topalg_1.html#E1:57"><i><font color="Green" title="E36">A1</font></i></a>, <a class="txt" href="topalg_1.html#E3:57"><i><font color="Green" title="E37">A3</font></i></a>, <a class="ref" href="eqrel_1.html#D5" title="EQREL_1:def.5">EQREL_1:def 5</a></i>;<br/>


</div>
