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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">A1</font>, <font color="Olive" title="b3">A2</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"><span class="p2">(<span class="default"><a href="setlim_1.html#K4" title="SETLIM_1:func.4">superior_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> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="setlim_1.html#K4" title="SETLIM_1:func.4">superior_setsequence</a> <font color="Olive" title="b3">A2</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 href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="setlim_1.html#K4" title="SETLIM_1:func.4">superior_setsequence</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">A1</font> <a href="setlim_2.html#K3" title="SETLIM_2:func.3">(\)</a> <font color="Olive" title="b3">A2</font></span>)</span></span>)</span> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Maroon" title="c1">n</font></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">A1</font>, <font color="Olive" title="b2">A2</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"><span class="p2">(<span class="default"><a href="setlim_1.html#K4" title="SETLIM_1:func.4">superior_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> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="setlim_1.html#K4" title="SETLIM_1:func.4">superior_setsequence</a> <font color="Olive" title="b2">A2</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 href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="setlim_1.html#K4" title="SETLIM_1:func.4">superior_setsequence</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">A1</font> <a href="setlim_2.html#K3" title="SETLIM_2:func.3">(\)</a> <font color="Olive" title="b2">A2</font></span>)</span></span>)</span> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Maroon" title="c1">n</font></span><br/><b>let </b><font color="Maroon" title="c3">A1</font>, <font color="Maroon" title="c4">A2</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"><span class="p2">(<span class="default"><a href="setlim_1.html#K4" title="SETLIM_1:func.4">superior_setsequence</a> <font color="Maroon" title="c3">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 href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="setlim_1.html#K4" title="SETLIM_1:func.4">superior_setsequence</a> <font color="Maroon" title="c4">A2</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 href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="setlim_1.html#K4" title="SETLIM_1:func.4">superior_setsequence</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A1</font> <a href="setlim_2.html#K3" title="SETLIM_2:func.3">(\)</a> <font color="Maroon" title="c4">A2</font></span>)</span></span>)</span> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Maroon" title="c1">n</font></span><br/>







<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="setlim_1.html#K4" title="SETLIM_1:func.4">superior_setsequence</a> <font color="Maroon" title="c3">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 href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="setlim_1.html#K4" title="SETLIM_1:func.4">superior_setsequence</a> <font color="Maroon" title="c4">A2</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 class="p1">(<span class="default"><a href="prob_1.html#K2" title="PROB_1:func.2">Union</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A1</font> <a href="nat_1.html#K7" title="NAT_1:func.7">^\</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="setlim_1.html#K4" title="SETLIM_1:func.4">superior_setsequence</a> <font color="Maroon" title="c4">A2</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#T2" target="_self" title="SETLIM_2:th.2">Th2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="prob_1.html#K2" title="PROB_1:func.2">Union</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A1</font> <a href="nat_1.html#K7" title="NAT_1:func.7">^\</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1">(<span class="default"><a href="prob_1.html#K2" title="PROB_1:func.2">Union</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">A2</font> <a href="nat_1.html#K7" title="NAT_1:func.7">^\</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="setlim_2.html#T2" target="_self" title="SETLIM_2:th.2">Th2</a></i>
;<br/>
<a NAME="E2:50"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="setlim_1.html#K4" title="SETLIM_1:func.4">superior_setsequence</a> <font color="Maroon" title="c3">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 href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="setlim_1.html#K4" title="SETLIM_1:func.4">superior_setsequence</a> <font color="Maroon" title="c4">A2</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 href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="prob_1.html#K2" title="PROB_1:func.2">Union</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">A1</font> <a href="nat_1.html#K7" title="NAT_1:func.7">^\</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="setlim_2.html#K3" title="SETLIM_2:func.3">(\)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">A2</font> <a href="nat_1.html#K7" title="NAT_1:func.7">^\</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="setlim_2.html#T10" target="_self" title="SETLIM_2:th.10">Th10</a></i>;<br/>
<a NAME="E3:50"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="setlim_1.html#K4" title="SETLIM_1:func.4">superior_setsequence</a> <font color="Maroon" title="c3">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 href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="setlim_1.html#K4" title="SETLIM_1:func.4">superior_setsequence</a> <font color="Maroon" title="c4">A2</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 href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="prob_1.html#K2" title="PROB_1:func.2">Union</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">A1</font> <a href="setlim_2.html#K3" title="SETLIM_2:func.3">(\)</a> <font color="Maroon" title="c4">A2</font></span>)</span> <a href="nat_1.html#K7" title="NAT_1:func.7">^\</a> <font color="Maroon" title="c1">n</font></span>)</span>
 
<b>by </b><i><a class="ref" href="setlim_2.html#T6" target="_self" title="SETLIM_2:th.6">Th6</a></i>;<br/>
<b>hence </b><a NAME="E4:50"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="setlim_1.html#K4" title="SETLIM_1:func.4">superior_setsequence</a> <font color="Maroon" title="c3">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 href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="setlim_1.html#K4" title="SETLIM_1:func.4">superior_setsequence</a> <font color="Maroon" title="c4">A2</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 href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="setlim_1.html#K4" title="SETLIM_1:func.4">superior_setsequence</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A1</font> <a href="setlim_2.html#K3" title="SETLIM_2:func.3">(\)</a> <font color="Maroon" title="c4">A2</font></span>)</span></span>)</span> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Maroon" title="c1">n</font>
 <b>by </b><i><a class="ref" href="setlim_2.html#T2" target="_self" title="SETLIM_2:th.2">Th2</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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