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<b>let </b><font color="Maroon">P</font> be   <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>;<br/><b>let </b><font color="Maroon">p</font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/><b>let </b><font color="Maroon">q</font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/>





<b>assume </b><a NAME="E1:7"/>
<font color="Maroon">P</font> <a href="topreal4.html#R1" target="_self">is_S-P_arc_joining</a> <font color="Maroon">p</font>,<font color="Maroon">q</font>
 ;<br/>

<a NAME="E2:7"/><b>then </b>
 ex <font color="Olive">h</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> st <br/>( <font color="Olive">h</font> <a href="topreal1.html#NR2" target="_self">is_S-Seq</a>  &amp; <font color="Maroon">P</font> <a href="hidden.html#R1">=</a>  <a href="topreal1.html#K5">L~</a> <font color="Olive">h</font> &amp; <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Olive">h</font> <a href="finseq_4.html#K4">/.</a> 1 &amp; <font color="Maroon">q</font> <a href="hidden.html#R1">=</a> <font color="Olive">h</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Olive">h</font></span>)</span> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:7"/>
<font color="Maroon">P</font> <a href="topreal1.html#R1">is_an_arc_of</a> <font color="Maroon">p</font>,<font color="Maroon">q</font>
 <b>by </b><i><a class="ref" href="topreal1.html#T31">TOPREAL1:31</a></i>;<br/>


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