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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="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">A1</font> being  <a href="prob_1.html#NM2" title="PROB_1:NM.2">SetSequence</a> of <font color="Maroon" title="c1">X</font> holds   <a href="kurato_2.html#K1" title="KURATO_2:func.1">Union</a> <span class="p1">(<span class="default"><a href="prob_3.html#K3" title="PROB_3:func.3">Partial_Diff_Union</a> <font color="Olive" title="b1">A1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="kurato_2.html#K1" title="KURATO_2:func.1">Union</a> <font color="Olive" title="b1">A1</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">A1</font> be   <a href="prob_1.html#NM2" title="PROB_1:NM.2">SetSequence</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="kurato_2.html#K1" title="KURATO_2:func.1">Union</a> <span class="p1">(<span class="default"><a href="prob_3.html#K3" title="PROB_3:func.3">Partial_Diff_Union</a> <font color="Maroon" title="c2">A1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="kurato_2.html#K1" title="KURATO_2:func.1">Union</a> <font color="Maroon" title="c2">A1</font></span><br/>



<span class="kw">thus </span> <a href="kurato_2.html#K1" title="KURATO_2:func.1">Union</a> <span class="p1">(<span class="default"><a href="prob_3.html#K3" title="PROB_3:func.3">Partial_Diff_Union</a> <font color="Maroon" title="c2">A1</font></span>)</span> = 
 <a href="kurato_2.html#K1" title="KURATO_2:func.1">Union</a> <span class="p1">(<span class="default"><a href="prob_3.html#K2" title="PROB_3:func.2">Partial_Union</a> <span class="p2">(<span class="default"><a href="prob_3.html#K3" title="PROB_3:func.3">Partial_Diff_Union</a> <font color="Maroon" title="c2">A1</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="prob_3.html#T17" target="_self" title="PROB_3:th.17">Th17</a></span>
<br/>.= 
 <a href="kurato_2.html#K1" title="KURATO_2:func.1">Union</a> <span class="p1">(<span class="default"><a href="prob_3.html#K2" title="PROB_3:func.2">Partial_Union</a> <font color="Maroon" title="c2">A1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="prob_3.html#T22" target="_self" title="PROB_3:th.22">Th22</a></span>
<br/>.= 
 <a href="kurato_2.html#K1" title="KURATO_2:func.1">Union</a> <font color="Maroon" title="c2">A1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="prob_3.html#T17" target="_self" title="PROB_3:th.17">Th17</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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