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<b>let </b><font color="Maroon" title="c1">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">A1</font> be   <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="15_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c3">n</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><a NAME="E1:15_1"/>
<span class="p1">(<span class="default"><a href="prob_3.html#K1" title="PROB_3:func.1">Partial_Intersection</a> <font color="Maroon" title="c2">A1</font></span>)</span> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="prob_3.html#K1" title="PROB_3:func.1">Partial_Intersection</a> <font color="Maroon" title="c2">A1</font></span>)</span> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A1</font> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="prob_3.html#D1" target="_self" title="PROB_3:def.1">Def1</a></i>;<br/><b>hence </b><a NAME="E2:15_1"/>
<span class="p1">(<span class="default"><a href="prob_3.html#K1" title="PROB_3:func.1">Partial_Intersection</a> <font color="Maroon" title="c2">A1</font></span>)</span> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="prob_3.html#K1" title="PROB_3:func.1">Partial_Intersection</a> <font color="Maroon" title="c2">A1</font></span>)</span> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Maroon" title="c3">n</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T17" title="XBOOLE_1:th.17">XBOOLE_1:17</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:15"/>
 <a href="prob_3.html#K1" title="PROB_3:func.1">Partial_Intersection</a> <font color="Maroon" title="c2">A1</font> is <a href="prob_1.html#V2" title="PROB_1:attr.2">non-increasing</a>
 <b>by </b><i><a class="ref" href="prob_2.html#T14" title="PROB_2:th.14">PROB_2:14</a></i>;<br/>


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