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<b>let </b><font color="Maroon" title="c1">r</font>, <font color="Maroon" title="c2">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="c3">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="c1">r</font>,<font color="Maroon" title="c2">s</font></span>)</span>;<br/><b>let </b><font color="Maroon" title="c4">C</font> be    <a href="rcomp_3.html#M1" title="RCOMP_3:mode.1">IntervalCover</a> of <font color="Maroon" title="c3">F</font>;<br/><b>let </b><font color="Maroon" title="c5">G</font> be    <a href="rcomp_3.html#M2" title="RCOMP_3:mode.2">IntervalCoverPts</a> of <font color="Maroon" title="c4">C</font>;<br/>









<b>assume </b><b>that </b><br/><a NAME="E1:87"/><i><font color="Green" title="E65">A1</font></i>: 
<font color="Maroon" title="c3">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="c1">r</font>,<font color="Maroon" title="c2">s</font>
 <b>and </b><br/><a NAME="E2:87"/><i><font color="Green" title="E66">A2</font></i>: 
<font color="Maroon" title="c3">F</font> is <a href="tops_2.html#V1" title="TOPS_2:attr.1">open</a>
 <b>and </b><br/><a NAME="E3:87"/><i><font color="Green" title="E67">A3</font></i>: 
<font color="Maroon" title="c3">F</font> is <a href="rcomp_3.html#V1" title="RCOMP_3:attr.1">connected</a>
 <b>and </b><br/><a NAME="E4:87"/><i><font color="Green" title="E68">A4</font></i>: 
<font color="Maroon" title="c1">r</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">s</font>
 ;<br/>

<a NAME="E5:87"/>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">C</font>
 
<b>by </b><i><a class="txt" href="rcomp_3.html#E1:87"><i><font color="Green" title="E65">A1</font></i></a>, <a class="txt" href="rcomp_3.html#E2:87"><i><font color="Green" title="E66">A2</font></i></a>, <a class="txt" href="rcomp_3.html#E3:87"><i><font color="Green" title="E67">A3</font></i></a>, <a class="txt" href="rcomp_3.html#E4:87"><i><font color="Green" title="E68">A4</font></i></a>, <a class="ref" href="rcomp_3.html#T65" target="_self" title="RCOMP_3:th.65">Th65</a></i>;<br/>
<a NAME="E6:87"/><b>then </b>
1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">C</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 
<b>by </b><i><a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a></i>;<br/>
<b>hence </b><a NAME="E7:87"/>
2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">G</font>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E1:87"><i><font color="Green" title="E65">A1</font></i></a>, <a class="txt" href="rcomp_3.html#E2:87"><i><font color="Green" title="E66">A2</font></i></a>, <a class="txt" href="rcomp_3.html#E3:87"><i><font color="Green" title="E67">A3</font></i></a>, <a class="txt" href="rcomp_3.html#E4:87"><i><font color="Green" title="E68">A4</font></i></a>, <a class="ref" href="rcomp_3.html#D3" target="_self" title="RCOMP_3:def.3">Def3</a></i>;<br/>


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