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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> ; <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">Si</font> being  <a href="prob_1.html#NM3" title="PROB_1:NM.3">SigmaField</a> of <font color="Maroon" title="c1">X</font><br/> for <font color="Olive" title="b2">S</font> being   <a href="prob_1.html#M1" title="PROB_1:mode.1">SetSequence</a> of <font color="Olive" title="b1">Si</font>  st <font color="Olive" title="b2">S</font> is <a href="setlim_1.html#V1" title="SETLIM_1:attr.1">monotone</a> holds <br/><font color="Olive" title="b2">S</font> is <a href="kurato_2.html#V3" title="KURATO_2:attr.3">convergent</a></span><br/><b>let </b><font color="Maroon" title="c2">Si</font> be   <a href="prob_1.html#NM3" title="PROB_1:NM.3">SigmaField</a> of <font color="Maroon" title="c1">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">S</font> being   <a href="prob_1.html#M1" title="PROB_1:mode.1">SetSequence</a> of <font color="Maroon" title="c2">Si</font>  st <font color="Olive" title="b1">S</font> is <a href="setlim_1.html#V1" title="SETLIM_1:attr.1">monotone</a> holds <br/><font color="Olive" title="b1">S</font> is <a href="kurato_2.html#V3" title="KURATO_2:attr.3">convergent</a></span><br/><b>let </b><font color="Maroon" title="c3">S</font> be    <a href="prob_1.html#M1" title="PROB_1:mode.1">SetSequence</a> of <font color="Maroon" title="c2">Si</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">S</font> is <a href="setlim_1.html#V1" title="SETLIM_1:attr.1">monotone</a> implies <font color="Maroon" title="c3">S</font> is <a href="kurato_2.html#V3" title="KURATO_2:attr.3">convergent</a> )</span><br/>





<b>assume </b><a NAME="E1:93"/><i><font color="Green" title="E63">AB</font></i>: 
<font color="Maroon" title="c3">S</font> is <a href="setlim_1.html#V1" title="SETLIM_1:attr.1">monotone</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">S</font> is <a href="kurato_2.html#V3" title="KURATO_2:attr.3">convergent</a></span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="93_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:93_1"/>
( <font color="Maroon" title="c3">S</font> is <a href="prob_1.html#V2" title="PROB_1:attr.2">non-ascending</a> or <font color="Maroon" title="c3">S</font> is <a href="prob_1.html#V3" title="PROB_1:attr.3">non-descending</a> )
 </span><b>by </b><i><a class="txt" href="#E1:93"><i><font color="Green" title="E63">AB</font></i></a>, <a class="ref" href="setlim_1.html#D1" target="_self" title="SETLIM_1:def.1">def1</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="93_1_1"><b>suppose </b></a><a NAME="E1:93_1_1"/>
<font color="Maroon" title="c3">S</font> is <a href="prob_1.html#V2" title="PROB_1:attr.2">non-ascending</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">S</font> is <a href="kurato_2.html#V3" title="KURATO_2:attr.3">convergent</a></span><br/><div class="add"><b>hence </b><a NAME="E2:93_1_1"/>
<font color="Maroon" title="c3">S</font> is <a href="kurato_2.html#V3" title="KURATO_2:attr.3">convergent</a>
 <b>by </b><i><a class="ref" href="setlim_1.html#T83" target="_self" title="SETLIM_1:th.83">Th66</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="93_1_2"><b>suppose </b></a><a NAME="E1:93_1_2"/>
<font color="Maroon" title="c3">S</font> is <a href="prob_1.html#V3" title="PROB_1:attr.3">non-descending</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">S</font> is <a href="kurato_2.html#V3" title="KURATO_2:attr.3">convergent</a></span><br/><div class="add"><b>hence </b><a NAME="E2:93_1_2"/>
<font color="Maroon" title="c3">S</font> is <a href="kurato_2.html#V3" title="KURATO_2:attr.3">convergent</a>
 <b>by </b><i><a class="ref" href="setlim_1.html#T80" target="_self" title="SETLIM_1:th.80">Th63</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div>

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