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<b>let </b><font color="Maroon" title="c1">P1</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">P1</font> is <a href="topreal1.html#V5" title="TOPREAL1:attr.5">being_S-P_arc</a> implies <font color="Maroon" title="c1">P1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )</span><br/>

<b>assume </b><a NAME="E1:43"/>
<font color="Maroon" title="c1">P1</font> is <a href="topreal1.html#V5" title="TOPREAL1:attr.5">being_S-P_arc</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">P1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><br/>

<b>then consider </b><font color="Maroon" title="c2">f</font> being   <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span><b> such that </b><br/><a NAME="E3:43"/><i><font color="Green" title="E30">A1</font></i>: 
( <font color="Maroon" title="c2">f</font> is <a href="topreal1.html#V4" title="TOPREAL1:attr.4">being_S-Seq</a> &amp; <font color="Maroon" title="c1">P1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c2">f</font> )
 <b>by </b><i><a class="ref" href="topreal1.html#D11" target="_self" title="TOPREAL1:def.11">Def11</a></i>;<br/>
<a NAME="E4:43"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">f</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 2
 
<b>by </b><i><a class="txt" href="#E3:43"><i><font color="Green" title="E30">A1</font></i></a>, <a class="ref" href="topreal1.html#D10" target="_self" title="TOPREAL1:def.10">Def10</a></i>;<br/>
<b>hence </b><a NAME="E5:43"/>
<font color="Maroon" title="c1">P1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="txt" href="#E3:43"><i><font color="Green" title="E30">A1</font></i></a>, <a class="ref" href="topreal1.html#T29" target="_self" title="TOPREAL1:th.29">Th29</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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