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<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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#K5" title="PROB_3:func.5">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/><span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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#K5" title="PROB_3:func.5">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/><span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="prob_3.html#K5" title="PROB_3:func.5">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/>





<span class="kw">consider </span><font color="Maroon" title="c4">ASeq</font> being   <a href="prob_1.html#NM4" title="PROB_1:NM.4">SetSequence</a> of <font color="Maroon" title="c2">Si</font><span class="kw"> such that </span><br/><a NAME="E2:55"/><span class="lab"><font color="Green" title="E45">A1</font></span>: 
( (  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#K1" title="RELSET_1:func.1">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#K8" title="PROB_3:func.8">.</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#K1" title="RELSET_1:func.1">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>  ) )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="prob_3.html#T56" target="_self" title="PROB_3:th.56">Th61</a></span>;<br/>
<a NAME="E3:55"/>
 <a href="kurato_0.html#K1" title="KURATO_0: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#K5" title="PROB_3:func.5">Union</a> <font color="Maroon" title="c3">FSi</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:55"><span class="lab"><font color="Green" title="E45">A1</font></span></a>, <a class="ref" href="prob_3.html#T55" target="_self" title="PROB_3:th.55">Th60</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:55"/>
 <a href="prob_3.html#K5" title="PROB_3:func.5">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 class="kw">by</span> <span class="lab"><a class="ref" href="prob_1.html#T17" title="PROB_1:th.17">PROB_1:17</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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