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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#K8" title="PROB_3:func.8">Union</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#K8" title="PROB_3:func.8">Union</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#K8" title="PROB_3:func.8">Union</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/>





<b>consider </b><font color="Maroon" title="c4">ASeq</font> being    <a href="prob_1.html#M1" title="PROB_1:mode.1">SetSequence</a> of <font color="Maroon" title="c2">Si</font><b> such that </b><br/><a NAME="E2:58"/><i><font color="Green" title="E50">A1</font></i>: 
( ( for <font color="Olive" title="b1">k</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">FSi</font> holds <br/><font color="Maroon" title="c4">ASeq</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">FSi</font> <a href="prob_3.html#K11" title="PROB_3:func.11">.</a> <font color="Olive" title="b1">k</font> ) &amp; ( for <font color="Olive" title="b1">k</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st not <font color="Olive" title="b1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">FSi</font> holds <br/><font color="Maroon" title="c4">ASeq</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</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#T61" target="_self" title="PROB_3:th.61">Th61</a></i>;<br/>
<a NAME="E3:58"/>
 <a href="kurato_2.html#K1" title="KURATO_2:func.1">Union</a> <font color="Maroon" title="c4">ASeq</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="prob_3.html#K8" title="PROB_3:func.8">Union</a> <font color="Maroon" title="c3">FSi</font>
 
<b>by </b><i><a class="txt" href="#E2:58"><i><font color="Green" title="E50">A1</font></i></a>, <a class="ref" href="prob_3.html#T60" target="_self" title="PROB_3:th.60">Th60</a></i>;<br/>
<b>hence </b><a NAME="E4:58"/>
 <a href="prob_3.html#K8" title="PROB_3:func.8">Union</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#T46" title="PROB_1:th.46">PROB_1:46</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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