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<span class="kw">let </span><font color="Maroon" title="c1">S</font> be   <a href="prob_1.html#NM2" title="PROB_1:NM.2">SetSequence</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">P</font> being  <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>  st <font color="Olive" title="b1">P</font> is  <a href="jordan2c.html#V1" title="JORDAN2C:attr.1">Bounded</a>  &amp; ( for <font color="Olive" title="b2">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <font color="Maroon" title="c1">S</font> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Olive" title="b2">i</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">P</font> ) holds <br/> <a href="kurato_2.html#K6" title="KURATO_2:func.6">Lim_inf</a> <font color="Maroon" title="c1">S</font> is  <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">P</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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">P</font> is  <a href="jordan2c.html#V1" title="JORDAN2C:attr.1">Bounded</a>  &amp; ( for <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <font color="Maroon" title="c1">S</font> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">P</font> ) implies  <a href="kurato_2.html#K6" title="KURATO_2:func.6">Lim_inf</a> <font color="Maroon" title="c1">S</font> is  <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a>  )</span><br/>



<span class="kw">assume </span><a NAME="E1:76"/>
( <font color="Maroon" title="c2">P</font> is  <a href="jordan2c.html#V1" title="JORDAN2C:attr.1">Bounded</a>  &amp; ( for <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <font color="Maroon" title="c1">S</font> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">P</font> ) )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="kurato_2.html#K6" title="KURATO_2:func.6">Lim_inf</a> <font color="Maroon" title="c1">S</font> is  <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a> </span><br/>

<a NAME="E2:76"/><span class="kw">then </span>
 <a href="kurato_2.html#K6" title="KURATO_2:func.6">Lim_inf</a> <font color="Maroon" title="c1">S</font> is  <a href="jordan2c.html#V1" title="JORDAN2C:attr.1">Bounded</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="kurato_2.html#T60" target="_self" title="KURATO_2:th.60">Th60</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:76"/>
 <a href="kurato_2.html#K6" title="KURATO_2:func.6">Lim_inf</a> <font color="Maroon" title="c1">S</font> is  <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="kurato_2.html#T50" target="_self" title="KURATO_2:th.50">Th50</a>, <a class="ref" href="topreal6.html#T88" title="TOPREAL6:th.88">TOPREAL6:88</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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