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

<b>consider </b><font color="Maroon">f1</font> being   <a href="struct_0.html#NM7">FinSequence</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>, <font color="Maroon">f2</font> being   <a href="struct_0.html#NM7">FinSequence</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span><b> such that </b><br/><a NAME="E2:47"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">f1</font> <a href="topreal1.html#NR2" target="_self">is_S-Seq</a>  &amp; <font color="Maroon">f2</font> <a href="topreal1.html#NR2" target="_self">is_S-Seq</a>  &amp;  <a href="topreal1.html#K2" target="_self">R^2-unit_square</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" target="_self">L~</a> <font color="Maroon">f1</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" target="_self">L~</a> <font color="Maroon">f2</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="topreal1.html#K5" target="_self">L~</a> <font color="Maroon">f1</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" target="_self">L~</a> <font color="Maroon">f2</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,0</span><a href="euclid.html#K23">]|</a></span>,<span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,1</span><a href="euclid.html#K23">]|</a></span></span><a href="tarski.html#K2">}</a></span> )
 <b>and </b><br/><a NAME="E3:47"/>
( <font color="Maroon">f1</font> <a href="finseq_4.html#K4">/.</a> 1 <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K23">|[</a><span class="default">0,0</span><a href="euclid.html#K23">]|</a></span> &amp; <font color="Maroon">f1</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f1</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K23">|[</a><span class="default">1,1</span><a href="euclid.html#K23">]|</a></span> &amp; <font color="Maroon">f2</font> <a href="finseq_4.html#K4">/.</a> 1 <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K23">|[</a><span class="default">0,0</span><a href="euclid.html#K23">]|</a></span> &amp; <font color="Maroon">f2</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f2</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K23">|[</a><span class="default">1,1</span><a href="euclid.html#K23">]|</a></span> )
 <b>by </b><i/>;<br/>
<b>reconsider </b><font color="Maroon">P1</font> =  <a href="topreal1.html#K5" target="_self">L~</a> <font color="Maroon">f1</font>, <font color="Maroon">P2</font> =  <a href="topreal1.html#K5" target="_self">L~</a> <font color="Maroon">f2</font> as  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <b>by </b><i/>;<br/>
<b>take </b>
<font color="Maroon">P1</font>
;<br/>

<b>take </b>
<font color="Maroon">P2</font>
;<br/>

<b>thus </b><a NAME="E5:47"/>
( <font color="Maroon">P1</font> <a href="topreal1.html#NR3" target="_self">is_S-P_arc</a>  &amp; <font color="Maroon">P2</font> <a href="topreal1.html#NR3" target="_self">is_S-P_arc</a>  &amp;  <a href="topreal1.html#K2" target="_self">R^2-unit_square</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">P1</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">P2</font> &amp; <font color="Maroon">P1</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">P2</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,0</span><a href="euclid.html#K23">]|</a></span>,<span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,1</span><a href="euclid.html#K23">]|</a></span></span><a href="tarski.html#K2">}</a></span> )
 <b>by </b><i>, </i>;<br/>


</div>
