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<b>let </b><font color="Maroon" title="c1">r</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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">F</font> being  <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="c1">r</font></span>)</span><br/> for <font color="Olive" title="b2">C</font> being   <a href="rcomp_3.html#M1" title="RCOMP_3:mode.1">IntervalCover</a> of <font color="Olive" title="b1">F</font>  st <font color="Olive" title="b1">F</font> is   <a href="struct_0.html#NM11" title="STRUCT_0:NM.11">Cover</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="c1">r</font></span>)</span> &amp; <font color="Olive" title="b1">F</font> is <a href="tops_2.html#V1" title="TOPS_2:attr.1">open</a> &amp; <font color="Olive" title="b1">F</font> is <a href="rcomp_3.html#V1" title="RCOMP_3:attr.1">connected</a> holds <br/><font color="Olive" title="b2">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="binarith.html#K11" title="BINARITH:func.11">&lt;*</a><span class="default"><span class="p2"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c1">r</font>,<font color="Maroon" title="c1">r</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span></span><a href="binarith.html#K11" title="BINARITH:func.11">*&gt;</a></span></span><br/>

<b>set </b><font color="Maroon" title="c2">L</font> =  <a href="topmetr.html#K4" title="TOPMETR:func.4">Closed-Interval-TSpace</a> <font color="Maroon" title="c1">r</font>,<font color="Maroon" title="c1">r</font>;<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="c1">r</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">C</font> being   <a href="rcomp_3.html#M1" title="RCOMP_3:mode.1">IntervalCover</a> of <font color="Maroon" title="c3">F</font>  st <font color="Maroon" title="c3">F</font> is   <a href="struct_0.html#NM11" title="STRUCT_0:NM.11">Cover</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="c1">r</font></span>)</span> &amp; <font color="Maroon" title="c3">F</font> is <a href="tops_2.html#V1" title="TOPS_2:attr.1">open</a> &amp; <font color="Maroon" title="c3">F</font> is <a href="rcomp_3.html#V1" title="RCOMP_3:attr.1">connected</a> holds <br/><font color="Olive" title="b1">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="binarith.html#K11" title="BINARITH:func.11">&lt;*</a><span class="default"><span class="p2"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c1">r</font>,<font color="Maroon" title="c1">r</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span></span><a href="binarith.html#K11" title="BINARITH:func.11">*&gt;</a></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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">F</font> is   <a href="struct_0.html#NM11" title="STRUCT_0:NM.11">Cover</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="c1">r</font></span>)</span> &amp; <font color="Maroon" title="c3">F</font> is <a href="tops_2.html#V1" title="TOPS_2:attr.1">open</a> &amp; <font color="Maroon" title="c3">F</font> is <a href="rcomp_3.html#V1" title="RCOMP_3:attr.1">connected</a> implies <font color="Maroon" title="c4">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="binarith.html#K11" title="BINARITH:func.11">&lt;*</a><span class="default"><span class="p2"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c1">r</font>,<font color="Maroon" title="c1">r</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span></span><a href="binarith.html#K11" title="BINARITH:func.11">*&gt;</a></span> )</span><br/>



<b>assume </b><b>that </b><br/><a NAME="E1:75"/><i><font color="Green" title="E58">A1</font></i>: 
<font color="Maroon" title="c3">F</font> is   <a href="struct_0.html#NM11" title="STRUCT_0:NM.11">Cover</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="c1">r</font></span>)</span>
 <b>and </b><br/><a NAME="E2:75"/><i><font color="Green" title="E59">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="E3:75"/><i><font color="Green" title="E60">A3</font></i>: 
<font color="Maroon" title="c3">F</font> is <a href="rcomp_3.html#V1" title="RCOMP_3:attr.1">connected</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="binarith.html#K11" title="BINARITH:func.11">&lt;*</a><span class="default"><span class="p2"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c1">r</font>,<font color="Maroon" title="c1">r</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span></span><a href="binarith.html#K11" title="BINARITH:func.11">*&gt;</a></span></span><br/>

<a NAME="E4:75"/><i><font color="Green" title="E61">A4</font></i>: 
<span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c1">r</font>,<font color="Maroon" title="c1">r</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="seq_4.html#K1" title="SEQ_4:func.1">{</a><span class="default"><font color="Maroon" title="c1">r</font></span><a href="seq_4.html#K1" title="SEQ_4:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="rcomp_1.html#T14" title="RCOMP_1:th.14">RCOMP_1:14</a></i>;<br/>
<a NAME="E5:75"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</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="c1">r</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c1">r</font>,<font color="Maroon" title="c1">r</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>
 
<b>by </b><i><a class="ref" href="topmetr.html#T25" title="TOPMETR:th.25">TOPMETR:25</a></i>;<br/>
<a NAME="E6:75"/><b>then </b>
<font color="Maroon" title="c1">r</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</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="c1">r</font></span>)</span>
 
<b>by </b><i><a class="txt" href="rcomp_3.html#E4:75"><i><font color="Green" title="E61">A4</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E7:75"/><b>then </b>
<span class="p1"><a href="seq_4.html#K1" title="SEQ_4:func.1">{</a><span class="default"><font color="Maroon" title="c1">r</font></span><a href="seq_4.html#K1" title="SEQ_4:func.1">}</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">F</font>
 
<b>by </b><i><a class="txt" href="rcomp_3.html#E1:75"><i><font color="Green" title="E58">A1</font></i></a>, <a class="ref" href="rcomp_3.html#T60" target="_self" title="RCOMP_3:th.60">Th60</a></i>;<br/>
<b>hence </b><a NAME="E8:75"/>
<font color="Maroon" title="c4">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="binarith.html#K11" title="BINARITH:func.11">&lt;*</a><span class="default"><span class="p2"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c1">r</font>,<font color="Maroon" title="c1">r</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span></span><a href="binarith.html#K11" title="BINARITH:func.11">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E1:75"><i><font color="Green" title="E58">A1</font></i></a>, <a class="txt" href="rcomp_3.html#E2:75"><i><font color="Green" title="E59">A2</font></i></a>, <a class="txt" href="rcomp_3.html#E3:75"><i><font color="Green" title="E60">A3</font></i></a>, <a class="txt" href="rcomp_3.html#E4:75"><i><font color="Green" title="E61">A4</font></i></a>, <a class="ref" href="rcomp_3.html#D2" target="_self" title="RCOMP_3:def.2">Def2</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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