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<span class="kw">let </span><font color="Maroon" title="c1">V</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">C</font> being  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <br/> for <font color="Olive" title="b2">u</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="substlat.html#K1" title="SUBSTLAT:func.1">SubstitutionSet</a> <font color="Maroon" title="c1">V</font>,<font color="Olive" title="b1">C</font> holds  <font color="Olive" title="b2">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattice2.html#K2" title="LATTICE2:func.2">FinJoin</a> <font color="Olive" title="b2">u</font>,<span class="p1">(<span class="default"><a href="heyting2.html#K8" title="HEYTING2:func.8">Atom</a> <font color="Maroon" title="c1">V</font>,<font color="Olive" title="b1">C</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">C</font> be   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>   <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">u</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="substlat.html#K1" title="SUBSTLAT:func.1">SubstitutionSet</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">C</font> holds  <font color="Olive" title="b1">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattice2.html#K2" title="LATTICE2:func.2">FinJoin</a> <font color="Olive" title="b1">u</font>,<span class="p1">(<span class="default"><a href="heyting2.html#K8" title="HEYTING2:func.8">Atom</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">C</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">u</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="substlat.html#K1" title="SUBSTLAT:func.1">SubstitutionSet</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">C</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattice2.html#K2" title="LATTICE2:func.2">FinJoin</a> <font color="Maroon" title="c3">u</font>,<span class="p1">(<span class="default"><a href="heyting2.html#K8" title="HEYTING2:func.8">Atom</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">C</font></span>)</span></span><br/>





<span class="kw">thus </span><font color="Maroon" title="c3">u</font> = 
 <a href="setwiseo.html#K10" title="SETWISEO:func.10">FinUnion</a> <font color="Maroon" title="c3">u</font>,<span class="p1">(<span class="default"><a href="setwiseo.html#K11" title="SETWISEO:func.11">singleton</a> <span class="p2">(<span class="default"><a href="partfun1.html#K4" title="PARTFUN1:func.4">PFuncs</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">C</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="setwiseo.html#T71" title="SETWISEO:th.71">SETWISEO:71</a></span>
<br/>.= 
 <a href="lattice2.html#K2" title="LATTICE2:func.2">FinJoin</a> <font color="Maroon" title="c3">u</font>,<span class="p1">(<span class="default"><a href="heyting2.html#K8" title="HEYTING2:func.8">Atom</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">C</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="heyting2.html#T23" target="_self" title="HEYTING2:th.23">Th23</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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