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<b>let </b><font color="Maroon" title="c8">r</font>, <font color="Maroon" title="c9">s</font> be  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ;<br/><b>let </b><font color="Maroon" title="c10">F</font> be   <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> <font color="Maroon" title="c8">r</font>,<font color="Maroon" title="c9">s</font></span>)</span>;<br/><b>let </b><font color="Maroon" title="c11">C</font> be    <a href="rcomp_3.html#M1" title="RCOMP_3:mode.1">IntervalCover</a> of <font color="Maroon" title="c10">F</font>;<br/><b>let </b><font color="Maroon" title="c12">G</font> be    <a href="rcomp_3.html#M2" title="RCOMP_3:mode.2">IntervalCoverPts</a> of <font color="Maroon" title="c11">C</font>;<br/>









<b>assume </b><a NAME="E1:37"/>
( <font color="Maroon" title="c10">F</font> <a href="pre_topc.html#R1" title="PRE_TOPC:pred.1">is_a_cover_of</a>  <a href="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> <font color="Maroon" title="c8">r</font>,<font color="Maroon" title="c9">s</font> &amp; <font color="Maroon" title="c10">F</font> is <a href="tops_2.html#V1" title="TOPS_2:attr.1">open</a> &amp; <font color="Maroon" title="c10">F</font> is <a href="rcomp_3.html#V1" title="RCOMP_3:attr.1">connected</a> &amp; <font color="Maroon" title="c8">r</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c9">s</font> )
 ;<br/>

<a NAME="E2:37"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c12">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c11">C</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 
<b>by </b><i><a class="ref" href="rcomp_3.html#D3" title="RCOMP_3:def.3">RCOMP_3:def 3</a></i>;<br/>
<b>hence </b><a NAME="E3:37"/>
not <font color="Maroon" title="c12">G</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 <b>by </b><i><a class="ref" href="finseq_1.html#T25" title="FINSEQ_1:th.25">FINSEQ_1:25</a></i>;<br/>


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