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<b>let </b><font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">c<sub>10</sub></font> be   <a href="struct_0.html#NM3">Subset-Family</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span>)</span>;<br/><b>let </b><font color="Maroon">c<sub>11</sub></font> be    <a href="rcomp_3.html#M1">IntervalCover</a> of <font color="Maroon">c<sub>10</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>12</sub></font> be    <a href="rcomp_3.html#M2">IntervalCoverPts</a> of <font color="Maroon">c<sub>11</sub></font>;<br/>









<b>assume </b><a NAME="E1:38"/>
( <font color="Maroon">c<sub>10</sub></font> <a href="pre_topc.html#R1">is_a_cover_of</a>  <a href="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font> is <a href="tops_2.html#V1">open</a> &amp; <font color="Maroon">c<sub>10</sub></font> is <a href="rcomp_3.html#V1">connected</a> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>9</sub></font> )
 ;<br/>

<a NAME="E2:38"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="rcomp_3.html#D3">RCOMP_3:def 3</a></i>;<br/>
<b>hence </b><a NAME="E3:38"/>
not <font color="Maroon">c<sub>12</sub></font> is <a href="xboole_0.html#V1">empty</a>
 <b>by </b><i><a class="ref" href="finseq_1.html#T25">FINSEQ_1:25</a></i>;<br/>


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