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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">FSi</font> being   <a href="prob_3.html#M1" title="PROB_3:mode.1">FinSequence</a> of <font color="Olive" title="b1">Si</font> holds   <a href="prob_3.html#K10" title="PROB_3:func.10">Intersection</a> <font color="Olive" title="b2">FSi</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">Si</font></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">FSi</font> being   <a href="prob_3.html#M1" title="PROB_3:mode.1">FinSequence</a> of <font color="Maroon" title="c2">Si</font> holds   <a href="prob_3.html#K10" title="PROB_3:func.10">Intersection</a> <font color="Olive" title="b1">FSi</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Si</font></span><br/><b>let </b><font color="Maroon" title="c3">FSi</font> be    <a href="prob_3.html#M1" title="PROB_3:mode.1">FinSequence</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">  <a href="prob_3.html#K10" title="PROB_3:func.10">Intersection</a> <font color="Maroon" title="c3">FSi</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Si</font></span><br/>





<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:60_1"/>
( <font color="Maroon" title="c3">FSi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  or <font color="Maroon" title="c3">FSi</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_1_1"><b>suppose </b></a><a NAME="E1:60_1_1"/>
<font color="Maroon" title="c3">FSi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="prob_3.html#K10" title="PROB_3:func.10">Intersection</a> <font color="Maroon" title="c3">FSi</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Si</font></span><br/><div class="add"><a NAME="E2:60_1_1"/><b>then </b>
 <a href="prob_3.html#K10" title="PROB_3:func.10">Intersection</a> <font color="Maroon" title="c3">FSi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="ref" href="prob_3.html#D9" target="_self" title="PROB_3:def.9">Def9</a></i>;<br/><b>hence </b><a NAME="E3:60_1_1"/>
 <a href="prob_3.html#K10" title="PROB_3:func.10">Intersection</a> <font color="Maroon" title="c3">FSi</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Si</font>
 <b>by </b><i><a class="ref" href="prob_1.html#T42" title="PROB_1:th.42">PROB_1:42</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="60_1_2"><b>suppose </b></a><a NAME="E1:60_1_2"/>
<font color="Maroon" title="c3">FSi</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="prob_3.html#K10" title="PROB_3:func.10">Intersection</a> <font color="Maroon" title="c3">FSi</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Si</font></span><br/><div class="add"><a NAME="E2:60_1_2"/><b>then </b><i><font color="Green" title="E50">A1</font></i>: 
 <a href="prob_3.html#K10" title="PROB_3:func.10">Intersection</a> <font color="Maroon" title="c3">FSi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="prob_3.html#K8" title="PROB_3:func.8">Union</a> <span class="p2">(<span class="default"><a href="prob_3.html#K12" title="PROB_3:func.12">@Complement</a> <font color="Maroon" title="c3">FSi</font></span>)</span></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="prob_3.html#D9" target="_self" title="PROB_3:def.9">Def9</a></i>;<br/><a NAME="E3:60_1_2"/>
 <a href="prob_3.html#K8" title="PROB_3:func.8">Union</a> <span class="p1">(<span class="default"><a href="prob_3.html#K12" title="PROB_3:func.12">@Complement</a> <font color="Maroon" title="c3">FSi</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Si</font>
 <b>by </b><i><a class="ref" href="prob_3.html#T62" target="_self" title="PROB_3:th.62">Th62</a></i>;<br/><b>hence </b><a NAME="E4:60_1_2"/>
 <a href="prob_3.html#K10" title="PROB_3:func.10">Intersection</a> <font color="Maroon" title="c3">FSi</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Si</font>
 <b>by </b><i><a class="txt" href="#E2:60_1_2"><i><font color="Green" title="E50">A1</font></i></a>, <a class="ref" href="prob_1.html#D1" title="PROB_1:def.1">PROB_1:def 1</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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