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<span class="kw">let </span><font color="Maroon" title="c1">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <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">A</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font><br/> for <font color="Olive" title="b2">A1</font> being  <a href="prob_1.html#NM2" title="PROB_1:NM.2">SetSequence</a> of <font color="Maroon" title="c1">X</font> holds   <a href="kurato_2.html#K3" title="KURATO_2:func.3">lim_inf</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">A</font> <a href="setlim_2.html#K5" title="SETLIM_2:func.5">(/\)</a> <font color="Olive" title="b2">A1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="kurato_2.html#K3" title="KURATO_2:func.3">lim_inf</a> <font color="Olive" title="b2">A1</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">A</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>; <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">A1</font> being  <a href="prob_1.html#NM2" title="PROB_1:NM.2">SetSequence</a> of <font color="Maroon" title="c1">X</font> holds   <a href="kurato_2.html#K3" title="KURATO_2:func.3">lim_inf</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="setlim_2.html#K5" title="SETLIM_2:func.5">(/\)</a> <font color="Olive" title="b1">A1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="kurato_2.html#K3" title="KURATO_2:func.3">lim_inf</a> <font color="Olive" title="b1">A1</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">A1</font> be   <a href="prob_1.html#NM2" title="PROB_1:NM.2">SetSequence</a> of <font color="Maroon" title="c1">X</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#K3" title="KURATO_2:func.3">lim_inf</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="setlim_2.html#K5" title="SETLIM_2:func.5">(/\)</a> <font color="Maroon" title="c3">A1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="kurato_2.html#K3" title="KURATO_2:func.3">lim_inf</a> <font color="Maroon" title="c3">A1</font></span>)</span></span><br/>





<span class="kw">reconsider </span><font color="Maroon" title="c4">X1</font> =  <a href="setlim_1.html#K2" title="SETLIM_1:func.2">inferior_setsequence</a> <font color="Maroon" title="c3">A1</font> as   <a href="prob_1.html#NM2" title="PROB_1:NM.2">SetSequence</a> of <font color="Maroon" title="c1">X</font> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c5">X2</font> =  <a href="setlim_1.html#K2" title="SETLIM_1:func.2">inferior_setsequence</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="setlim_2.html#K5" title="SETLIM_2:func.5">(/\)</a> <font color="Maroon" title="c3">A1</font></span>)</span> as   <a href="prob_1.html#NM2" title="PROB_1:NM.2">SetSequence</a> of <font color="Maroon" title="c1">X</font> ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="76_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c6">n</font> be    <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> ; <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="c5">X2</font> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Maroon" title="c6">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="setlim_2.html#K5" title="SETLIM_2:func.5">(/\)</a> <font color="Maroon" title="c4">X1</font></span>)</span> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Maroon" title="c6">n</font></span><br/><span class="kw">thus </span><font color="Maroon" title="c5">X2</font> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Maroon" title="c6">n</font> = 
<font color="Maroon" title="c2">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">X1</font> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Maroon" title="c6">n</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="setlim_2.html#T50" target="_self" title="SETLIM_2:th.50">Th50</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="setlim_2.html#K5" title="SETLIM_2:func.5">(/\)</a> <font color="Maroon" title="c4">X1</font></span>)</span> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Maroon" title="c6">n</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="setlim_2.html#D5" target="_self" title="SETLIM_2:def.5">Def5</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/></div><span class="kw">end;</span></div>
<a NAME="E4:76"/><span class="kw">then </span>
<font color="Maroon" title="c5">X2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">A</font> <a href="setlim_2.html#K5" title="SETLIM_2:func.5">(/\)</a> <font color="Maroon" title="c4">X1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T113" title="FUNCT_2:th.113">FUNCT_2:113</a></span>;<br/>
<a NAME="E5:76"/><span class="kw">then </span>
 <a href="prob_1.html#K2" title="PROB_1:func.2">Union</a> <font color="Maroon" title="c5">X2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="prob_1.html#K2" title="PROB_1:func.2">Union</a> <font color="Maroon" title="c4">X1</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="setlim_2.html#T38" target="_self" title="SETLIM_2:th.38">Th38</a></span>;<br/>
<a NAME="E6:76"/><span class="kw">then </span>
 <a href="kurato_2.html#K3" title="KURATO_2:func.3">lim_inf</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="setlim_2.html#K5" title="SETLIM_2:func.5">(/\)</a> <font color="Maroon" title="c3">A1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="prob_1.html#K2" title="PROB_1:func.2">Union</a> <font color="Maroon" title="c4">X1</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="setlim_1.html#D4" title="SETLIM_1:def.4">SETLIM_1:def 4</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:76"/>
 <a href="kurato_2.html#K3" title="KURATO_2:func.3">lim_inf</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="setlim_2.html#K5" title="SETLIM_2:func.5">(/\)</a> <font color="Maroon" title="c3">A1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="kurato_2.html#K3" title="KURATO_2:func.3">lim_inf</a> <font color="Maroon" title="c3">A1</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="setlim_1.html#D4" title="SETLIM_1:def.4">SETLIM_1:def 4</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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