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<b>let </b><font color="Maroon" title="c1">Omega</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">Sigma</font> be   <a href="prob_1.html#NM3" title="PROB_1:NM.3">SigmaField</a> of <font color="Maroon" title="c1">Omega</font>;<br/><b>let </b><font color="Maroon" title="c3">ASeq</font>, <font color="Maroon" title="c4">BSeq</font> be    <a href="prob_1.html#M1" title="PROB_1:mode.1">SetSequence</a> of <font color="Maroon" title="c2">Sigma</font>;<br/><b>let </b><font color="Maroon" title="c5">B</font> be    <a href="prob_1.html#M2" title="PROB_1:mode.2">Event</a> of <font color="Maroon" title="c2">Sigma</font>;<br/>









<b>assume </b><a NAME="E1:6"/><i><font color="Green" title="E6">A1</font></i>: 
( <font color="Maroon" title="c3">ASeq</font> is <a href="prob_1.html#V2" title="PROB_1:attr.2">non-increasing</a> &amp; ( for <font color="Olive" title="b1">n</font> being   <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>  holds  <font color="Maroon" title="c4">BSeq</font> <a href="prob_2.html#K1" title="PROB_2:func.1">.</a> <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">ASeq</font> <a href="prob_2.html#K1" title="PROB_2:func.1">.</a> <font color="Olive" title="b1">n</font></span>)</span> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Maroon" title="c5">B</font> ) )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c6">m</font>, <font color="Maroon" title="c7">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/><b>assume </b><a NAME="E1:6_1"/>
<font color="Maroon" title="c6">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c7">n</font>
 ;<br/><a NAME="E2:6_1"/><b>then </b>
<font color="Maroon" title="c3">ASeq</font> <a href="prob_2.html#K1" title="PROB_2:func.1">.</a> <font color="Maroon" title="c7">n</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">ASeq</font> <a href="prob_2.html#K1" title="PROB_2:func.1">.</a> <font color="Maroon" title="c6">m</font>
 <b>by </b><i><a class="txt" href="prob_2.html#E1:6"><i><font color="Green" title="E6">A1</font></i></a>, <a class="ref" href="prob_1.html#D6" title="PROB_1:def.6">PROB_1:def 6</a></i>;<br/><a NAME="E3:6_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">ASeq</font> <a href="prob_2.html#K1" title="PROB_2:func.1">.</a> <font color="Maroon" title="c7">n</font></span>)</span> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Maroon" title="c5">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">ASeq</font> <a href="prob_2.html#K1" title="PROB_2:func.1">.</a> <font color="Maroon" title="c6">m</font></span>)</span> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Maroon" title="c5">B</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T26" title="XBOOLE_1:th.26">XBOOLE_1:26</a></i>;<br/><a NAME="E4:6_1"/><b>then </b>
<font color="Maroon" title="c4">BSeq</font> <a href="prob_2.html#K1" title="PROB_2:func.1">.</a> <font color="Maroon" title="c7">n</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">ASeq</font> <a href="prob_2.html#K1" title="PROB_2:func.1">.</a> <font color="Maroon" title="c6">m</font></span>)</span> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Maroon" title="c5">B</font>
 <b>by </b><i><a class="txt" href="prob_2.html#E1:6"><i><font color="Green" title="E6">A1</font></i></a></i>;<br/><b>hence </b><a NAME="E5:6_1"/>
<font color="Maroon" title="c4">BSeq</font> <a href="prob_2.html#K1" title="PROB_2:func.1">.</a> <font color="Maroon" title="c7">n</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">BSeq</font> <a href="prob_2.html#K1" title="PROB_2:func.1">.</a> <font color="Maroon" title="c6">m</font>
 <b>by </b><i><a class="txt" href="prob_2.html#E1:6"><i><font color="Green" title="E6">A1</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:6"/>
<font color="Maroon" title="c4">BSeq</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_1.html#D6" title="PROB_1:def.6">PROB_1:def 6</a></i>;<br/>


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