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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="prob_1.html#NM2">SetSequence</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>







<span class="p1">(<span class="default"><a href="setlim_1.html#K1">inferior_setsequence</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="setlim_2.html#K3" target="_self">(\)</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="prob_1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font> = 
 <a href="prob_1.html#K4">Intersection</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="setlim_2.html#K3" target="_self">(\)</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="kurato_2.html#K3">^\</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="setlim_2.html#T1" target="_self">Th1</a></i>
<br/>.= 
 <a href="prob_1.html#K4">Intersection</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="kurato_2.html#K3">^\</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="setlim_2.html#K3" target="_self">(\)</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="kurato_2.html#K3">^\</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="setlim_2.html#T6" target="_self">Th6</a></i>
;<br/>
<a NAME="E2:47"/><b>then </b>
<span class="p1">(<span class="default"><a href="setlim_1.html#K1">inferior_setsequence</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="setlim_2.html#K3" target="_self">(\)</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="prob_1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="prob_1.html#K4">Intersection</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="kurato_2.html#K3">^\</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><a href="prob_1.html#K4">Intersection</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="kurato_2.html#K3">^\</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="setlim_2.html#T14" target="_self">Th14</a></i>;<br/>
<a NAME="E3:47"/><b>then </b>
<span class="p1">(<span class="default"><a href="setlim_1.html#K1">inferior_setsequence</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="setlim_2.html#K3" target="_self">(\)</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="prob_1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="setlim_1.html#K1">inferior_setsequence</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="prob_1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><a href="prob_1.html#K4">Intersection</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="kurato_2.html#K3">^\</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="setlim_2.html#T1" target="_self">Th1</a></i>;<br/>
<b>hence </b><a NAME="E4:47"/>
<span class="p1">(<span class="default"><a href="setlim_1.html#K1">inferior_setsequence</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="setlim_2.html#K3" target="_self">(\)</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="prob_1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="setlim_1.html#K1">inferior_setsequence</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="prob_1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="setlim_1.html#K1">inferior_setsequence</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="prob_1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="setlim_2.html#T1" target="_self">Th1</a></i>;<br/>


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