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<b>let </b><font color="Maroon" title="c1">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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">X</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <br/> for <font color="Olive" title="b2">A</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Olive" title="b1">X</font><br/> for <font color="Olive" title="b3">A1</font> being  <a href="prob_1.html#NM2" title="PROB_1:NM.2">SetSequence</a> of <font color="Olive" title="b1">X</font> holds  <span class="p1">(<span class="default"><a href="setlim_1.html#K2" title="SETLIM_1:func.2">inferior_setsequence</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">A</font> <a href="setlim_2.html#K6" title="SETLIM_2:func.6">(\/)</a> <font color="Olive" title="b3">A1</font></span>)</span></span>)</span> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">A</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="setlim_1.html#K2" title="SETLIM_1:func.2">inferior_setsequence</a> <font color="Olive" title="b3">A1</font></span>)</span> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Maroon" title="c1">n</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</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">A</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c2">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="c2">X</font> holds  <span class="p1">(<span class="default"><a href="setlim_1.html#K2" title="SETLIM_1:func.2">inferior_setsequence</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">A</font> <a href="setlim_2.html#K6" title="SETLIM_2:func.6">(\/)</a> <font color="Olive" title="b2">A1</font></span>)</span></span>)</span> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">A</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="setlim_1.html#K2" title="SETLIM_1:func.2">inferior_setsequence</a> <font color="Olive" title="b2">A1</font></span>)</span> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Maroon" title="c1">n</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c3">A</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c2">X</font>; <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">A1</font> being  <a href="prob_1.html#NM2" title="PROB_1:NM.2">SetSequence</a> of <font color="Maroon" title="c2">X</font> holds  <span class="p1">(<span class="default"><a href="setlim_1.html#K2" title="SETLIM_1:func.2">inferior_setsequence</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="setlim_2.html#K6" title="SETLIM_2:func.6">(\/)</a> <font color="Olive" title="b1">A1</font></span>)</span></span>)</span> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">A</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="setlim_1.html#K2" title="SETLIM_1:func.2">inferior_setsequence</a> <font color="Olive" title="b1">A1</font></span>)</span> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Maroon" title="c1">n</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c4">A1</font> be   <a href="prob_1.html#NM2" title="PROB_1:NM.2">SetSequence</a> of <font color="Maroon" title="c2">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="setlim_1.html#K2" title="SETLIM_1:func.2">inferior_setsequence</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="setlim_2.html#K6" title="SETLIM_2:func.6">(\/)</a> <font color="Maroon" title="c4">A1</font></span>)</span></span>)</span> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">A</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="setlim_1.html#K2" title="SETLIM_1:func.2">inferior_setsequence</a> <font color="Maroon" title="c4">A1</font></span>)</span> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Maroon" title="c1">n</font></span>)</span></span><br/>







<span class="p1">(<span class="default"><a href="setlim_1.html#K2" title="SETLIM_1:func.2">inferior_setsequence</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="setlim_2.html#K6" title="SETLIM_2:func.6">(\/)</a> <font color="Maroon" title="c4">A1</font></span>)</span></span>)</span> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Maroon" title="c1">n</font> = 
 <a href="prob_1.html#K4" title="PROB_1:func.4">Intersection</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="setlim_2.html#K6" title="SETLIM_2:func.6">(\/)</a> <font color="Maroon" title="c4">A1</font></span>)</span> <a href="kurato_2.html#K3" title="KURATO_2:func.3">^\</a> <font color="Maroon" title="c1">n</font></span>)</span>
<b>by </b><i><a class="ref" href="setlim_2.html#T1" target="_self" title="SETLIM_2:th.1">Th1</a></i>
<br/>.= 
 <a href="prob_1.html#K4" title="PROB_1:func.4">Intersection</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="setlim_2.html#K6" title="SETLIM_2:func.6">(\/)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">A1</font> <a href="kurato_2.html#K3" title="KURATO_2:func.3">^\</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="setlim_2.html#T17" target="_self" title="SETLIM_2:th.17">Th17</a></i>
<br/>.= 
<font color="Maroon" title="c3">A</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="prob_1.html#K4" title="PROB_1:func.4">Intersection</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">A1</font> <a href="kurato_2.html#K3" title="KURATO_2:func.3">^\</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="setlim_2.html#T34" target="_self" title="SETLIM_2:th.34">Th34</a></i>
<br/>.= 
<font color="Maroon" title="c3">A</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="setlim_1.html#K2" title="SETLIM_1:func.2">inferior_setsequence</a> <font color="Maroon" title="c4">A1</font></span>)</span> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Maroon" title="c1">n</font></span>)</span>
<b>by </b><i><a class="ref" href="setlim_2.html#T1" target="_self" title="SETLIM_2:th.1">Th1</a></i>
;<br/>
<b>hence </b><a NAME="E2:53"/>
<span class="p1">(<span class="default"><a href="setlim_1.html#K2" title="SETLIM_1:func.2">inferior_setsequence</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="setlim_2.html#K6" title="SETLIM_2:func.6">(\/)</a> <font color="Maroon" title="c4">A1</font></span>)</span></span>)</span> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">A</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="setlim_1.html#K2" title="SETLIM_1:func.2">inferior_setsequence</a> <font color="Maroon" title="c4">A1</font></span>)</span> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Maroon" title="c1">n</font></span>)</span>
 ; <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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