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<span class="kw">let </span><font color="Maroon" title="c1">V</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">A</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   <a href="substlat.html#K3" title="SUBSTLAT:func.3">mi</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">A</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <span class="p2">(<span class="default"><a href="heyting2.html#K2" title="HEYTING2:func.2">-</a> <font color="Olive" title="b2">A</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <span class="p1">(<span class="default"><a href="substlat.html#K5" title="SUBSTLAT:func.5">SubstLatt</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#M2" title="HIDDEN:mode.2">set</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">A</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   <a href="substlat.html#K3" title="SUBSTLAT:func.3">mi</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">A</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <span class="p2">(<span class="default"><a href="heyting2.html#K2" title="HEYTING2:func.2">-</a> <font color="Olive" title="b1">A</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <span class="p1">(<span class="default"><a href="substlat.html#K5" title="SUBSTLAT:func.5">SubstLatt</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">A</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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="substlat.html#K3" title="SUBSTLAT:func.3">mi</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <span class="p2">(<span class="default"><a href="heyting2.html#K2" title="HEYTING2:func.2">-</a> <font color="Maroon" title="c3">A</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <span class="p1">(<span class="default"><a href="substlat.html#K5" title="SUBSTLAT:func.5">SubstLatt</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">C</font>)</span>)</span></span><br/>





 <a href="substlat.html#K3" title="SUBSTLAT:func.3">mi</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <span class="p2">(<span class="default"><a href="heyting2.html#K2" title="HEYTING2:func.2">-</a> <font color="Maroon" title="c3">A</font></span>)</span></span>)</span> = 
 <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="heyting2.html#T9" target="_self" onmouseover="rs('heyting2/T9')" onmouseout="rh()">Th9</a>, <a class="ref" href="substlat.html#T9" onmouseover="rs('substlat/T9')" onmouseout="rh()">SUBSTLAT:9</a></span>
<br/>.= 
 <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <span class="p1">(<span class="default"><a href="substlat.html#K5" title="SUBSTLAT:func.5">SubstLatt</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="substlat.html#T26" onmouseover="rs('substlat/T26')" onmouseout="rh()">SUBSTLAT:26</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E2:15"/>
 <a href="substlat.html#K3" title="SUBSTLAT:func.3">mi</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <span class="p2">(<span class="default"><a href="heyting2.html#K2" title="HEYTING2:func.2">-</a> <font color="Maroon" title="c3">A</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <span class="p1">(<span class="default"><a href="substlat.html#K5" title="SUBSTLAT:func.5">SubstLatt</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">C</font>)</span>)</span>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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