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<b>let </b><font color="Maroon" title="c1">S</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> non <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>  <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</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">A</font> being <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a>  <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c1">S</font><br/> for <font color="Olive" title="b2">X</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K6" title="MSUALG_5:func.6">CongrLatt</a> <font color="Olive" title="b1">A</font></span>)</span> holds   <a href="lattice3.html#K15" title="LATTICE3:func.15">"\/"</a> <font color="Olive" title="b2">X</font>,<span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Olive" title="b1">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattice3.html#K15" title="LATTICE3:func.15">"\/"</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="lattice3.html#K15" title="LATTICE3:func.15">"\/"</a> <font color="Olive" title="b3">X0</font>,<span class="p3">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Olive" title="b1">A</font></span>)</span></span>)</span> where <font color="Olive" title="b3">X0</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Olive" title="b1">A</font></span>)</span> : <font color="Olive" title="b3">X0</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Olive" title="b2">X</font> </span>}</span> ,<span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Olive" title="b1">A</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">A</font> be  <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a>  <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c1">S</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">X</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K6" title="MSUALG_5:func.6">CongrLatt</a> <font color="Maroon" title="c2">A</font></span>)</span> holds   <a href="lattice3.html#K15" title="LATTICE3:func.15">"\/"</a> <font color="Olive" title="b1">X</font>,<span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattice3.html#K15" title="LATTICE3:func.15">"\/"</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="lattice3.html#K15" title="LATTICE3:func.15">"\/"</a> <font color="Olive" title="b2">X0</font>,<span class="p3">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span></span>)</span> where <font color="Olive" title="b2">X0</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> : <font color="Olive" title="b2">X0</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Olive" title="b1">X</font> </span>}</span> ,<span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c3">X</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K6" title="MSUALG_5:func.6">CongrLatt</a> <font color="Maroon" title="c2">A</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="lattice3.html#K15" title="LATTICE3:func.15">"\/"</a> <font color="Maroon" title="c3">X</font>,<span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattice3.html#K15" title="LATTICE3:func.15">"\/"</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="lattice3.html#K15" title="LATTICE3:func.15">"\/"</a> <font color="Olive" title="b1">X0</font>,<span class="p3">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span></span>)</span> where <font color="Olive" title="b1">X0</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> : <font color="Olive" title="b1">X0</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">X</font> </span>}</span> ,<span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span></span><br/>





<b>set </b><font color="Maroon" title="c4">E</font> =  <a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font>;<br/>
<b>set </b><font color="Maroon" title="c5">X1</font> = <span class="p1">{<span class="default"> <font color="Olive" title="b1">X0</font> where <font color="Olive" title="b1">X0</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> : <font color="Olive" title="b1">X0</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">X</font> </span>}</span> ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c6">i</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"> ( <font color="Maroon" title="c6">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">X0</font> where <font color="Olive" title="b1">X0</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> : <font color="Olive" title="b1">X0</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">X</font> </span>}</span>  implies <font color="Maroon" title="c6">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> )</span><br/><b>assume </b><a NAME="E1:20_1"/>
<font color="Maroon" title="c6">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">X0</font> where <font color="Olive" title="b1">X0</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> : <font color="Olive" title="b1">X0</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">X</font> </span>}</span> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c6">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span></span><br/><b>then consider </b><font color="Maroon" title="c7">I1</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span><b> such that </b><br/><a NAME="E3:20_1"/><i><font color="Green" title="E10">A1</font></i>: 
( <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">I1</font> &amp; <font color="Maroon" title="c7">I1</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">X</font> )
 ;<br/><b>thus </b><a NAME="E4:20_1"/>
<font color="Maroon" title="c6">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E3:20_1"><i><font color="Green" title="E10">A1</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<a NAME="E2:20"/><b>then </b><i><font color="Green" title="E10">A2</font></i>: 
<span class="p1">{<span class="default"> <font color="Olive" title="b1">X0</font> where <font color="Olive" title="b1">X0</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> : <font color="Olive" title="b1">X0</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">X</font> </span>}</span>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span>
 
<b>by </b><i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/>
<b>set </b><font color="Maroon" title="c6">B1</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="lattice3.html#NK17" title="LATTICE3:NK.17">"\/"</a> <font color="Olive" title="b1">Y</font></span>)</span> where <font color="Olive" title="b1">Y</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> : <font color="Olive" title="b1">Y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b2">X0</font> where <font color="Olive" title="b2">X0</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> : <font color="Olive" title="b2">X0</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">X</font> </span>}</span>  </span>}</span> ;<br/>
<b>set </b><font color="Maroon" title="c7">B2</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="lattice3.html#K15" title="LATTICE3:func.15">"\/"</a> <font color="Olive" title="b1">X0</font>,<span class="p3">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span></span>)</span> where <font color="Olive" title="b1">X0</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> : <font color="Olive" title="b1">X0</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">X</font> </span>}</span> ;<br/>
<a NAME="E3:20"/><i><font color="Green" title="E11">A3</font></i>: 
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="lattice3.html#NK17" title="LATTICE3:NK.17">"\/"</a> <font color="Olive" title="b1">Y</font></span>)</span> where <font color="Olive" title="b1">Y</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> : <font color="Olive" title="b1">Y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b2">X0</font> where <font color="Olive" title="b2">X0</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> : <font color="Olive" title="b2">X0</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">X</font> </span>}</span>  </span>}</span>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="lattice3.html#K15" title="LATTICE3:func.15">"\/"</a> <font color="Olive" title="b1">X0</font>,<span class="p3">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span></span>)</span> where <font color="Olive" title="b1">X0</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> : <font color="Olive" title="b1">X0</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">X</font> </span>}</span> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_2"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:20_2"/>
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="lattice3.html#NK17" title="LATTICE3:NK.17">"\/"</a> <font color="Olive" title="b1">Y</font></span>)</span> where <font color="Olive" title="b1">Y</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> : <font color="Olive" title="b1">Y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b2">X0</font> where <font color="Olive" title="b2">X0</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> : <font color="Olive" title="b2">X0</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">X</font> </span>}</span>  </span>}</span>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="lattice3.html#K15" title="LATTICE3:func.15">"\/"</a> <font color="Olive" title="b1">X0</font>,<span class="p3">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span></span>)</span> where <font color="Olive" title="b1">X0</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> : <font color="Olive" title="b1">X0</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">X</font> </span>}</span> 
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="lattice3.html#K15" title="LATTICE3:func.15">"\/"</a> <font color="Olive" title="b1">X0</font>,<span class="p3">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span></span>)</span> where <font color="Olive" title="b1">X0</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> : <font color="Olive" title="b1">X0</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">X</font> </span>}</span>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="lattice3.html#NK17" title="LATTICE3:NK.17">"\/"</a> <font color="Olive" title="b1">Y</font></span>)</span> where <font color="Olive" title="b1">Y</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> : <font color="Olive" title="b1">Y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b2">X0</font> where <font color="Olive" title="b2">X0</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> : <font color="Olive" title="b2">X0</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">X</font> </span>}</span>  </span>}</span> </span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c8">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="lattice3.html#NK17" title="LATTICE3:NK.17">"\/"</a> <font color="Olive" title="b1">Y</font></span>)</span> where <font color="Olive" title="b1">Y</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> : <font color="Olive" title="b1">Y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b2">X0</font> where <font color="Olive" title="b2">X0</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> : <font color="Olive" title="b2">X0</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">X</font> </span>}</span>  </span>}</span>  or <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="lattice3.html#K15" title="LATTICE3:func.15">"\/"</a> <font color="Olive" title="b1">X0</font>,<span class="p3">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span></span>)</span> where <font color="Olive" title="b1">X0</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> : <font color="Olive" title="b1">X0</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">X</font> </span>}</span>  )</span><br/>

<b>assume </b><a NAME="E1:20_2_1"/>
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="lattice3.html#NK17" title="LATTICE3:NK.17">"\/"</a> <font color="Olive" title="b1">Y</font></span>)</span> where <font color="Olive" title="b1">Y</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> : <font color="Olive" title="b1">Y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b2">X0</font> where <font color="Olive" title="b2">X0</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> : <font color="Olive" title="b2">X0</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">X</font> </span>}</span>  </span>}</span> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="lattice3.html#K15" title="LATTICE3:func.15">"\/"</a> <font color="Olive" title="b1">X0</font>,<span class="p3">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span></span>)</span> where <font color="Olive" title="b1">X0</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> : <font color="Olive" title="b1">X0</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">X</font> </span>}</span> </span><br/>

<b>then consider </b><font color="Maroon" title="c9">Y1</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span><b> such that </b><br/><a NAME="E3:20_2_1"/><i><font color="Green" title="E12">A4</font></i>: 
( <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattice3.html#NK17" title="LATTICE3:NK.17">"\/"</a> <font color="Maroon" title="c9">Y1</font> &amp; <font color="Maroon" title="c9">Y1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">X0</font> where <font color="Olive" title="b1">X0</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> : <font color="Olive" title="b1">X0</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">X</font> </span>}</span>  )
 ;<br/>
<b>consider </b><font color="Maroon" title="c10">Y2</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span><b> such that </b><br/><a NAME="E5:20_2_1"/><i><font color="Green" title="E13">A5</font></i>: 
( <font color="Maroon" title="c9">Y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">Y2</font> &amp; <font color="Maroon" title="c10">Y2</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">X</font> )
 <b>by </b><i><a class="txt" href="#E3:20_2_1"><i><font color="Green" title="E12">A4</font></i></a></i>;<br/>
<b>thus </b><a NAME="E6:20_2_1"/>
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="lattice3.html#K15" title="LATTICE3:func.15">"\/"</a> <font color="Olive" title="b1">X0</font>,<span class="p3">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span></span>)</span> where <font color="Olive" title="b1">X0</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> : <font color="Olive" title="b1">X0</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">X</font> </span>}</span> 
 <b>by </b><i><a class="txt" href="#E3:20_2_1"><i><font color="Green" title="E12">A4</font></i></a>, <a class="txt" href="#E5:20_2_1"><i><font color="Green" title="E13">A5</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E2:20_2"/>
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="lattice3.html#K15" title="LATTICE3:func.15">"\/"</a> <font color="Olive" title="b1">X0</font>,<span class="p3">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span></span>)</span> where <font color="Olive" title="b1">X0</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> : <font color="Olive" title="b1">X0</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">X</font> </span>}</span>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="lattice3.html#NK17" title="LATTICE3:NK.17">"\/"</a> <font color="Olive" title="b1">Y</font></span>)</span> where <font color="Olive" title="b1">Y</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> : <font color="Olive" title="b1">Y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b2">X0</font> where <font color="Olive" title="b2">X0</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> : <font color="Olive" title="b2">X0</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">X</font> </span>}</span>  </span>}</span> 
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_2_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c8">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="lattice3.html#K15" title="LATTICE3:func.15">"\/"</a> <font color="Olive" title="b1">X0</font>,<span class="p3">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span></span>)</span> where <font color="Olive" title="b1">X0</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> : <font color="Olive" title="b1">X0</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">X</font> </span>}</span>  or <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="lattice3.html#NK17" title="LATTICE3:NK.17">"\/"</a> <font color="Olive" title="b1">Y</font></span>)</span> where <font color="Olive" title="b1">Y</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> : <font color="Olive" title="b1">Y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b2">X0</font> where <font color="Olive" title="b2">X0</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> : <font color="Olive" title="b2">X0</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">X</font> </span>}</span>  </span>}</span>  )</span><br/>

<b>assume </b><a NAME="E1:20_2_2"/>
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="lattice3.html#K15" title="LATTICE3:func.15">"\/"</a> <font color="Olive" title="b1">X0</font>,<span class="p3">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span></span>)</span> where <font color="Olive" title="b1">X0</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> : <font color="Olive" title="b1">X0</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">X</font> </span>}</span> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="lattice3.html#NK17" title="LATTICE3:NK.17">"\/"</a> <font color="Olive" title="b1">Y</font></span>)</span> where <font color="Olive" title="b1">Y</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> : <font color="Olive" title="b1">Y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b2">X0</font> where <font color="Olive" title="b2">X0</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> : <font color="Olive" title="b2">X0</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">X</font> </span>}</span>  </span>}</span> </span><br/>

<b>then consider </b><font color="Maroon" title="c9">Y1</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span><b> such that </b><br/><a NAME="E3:20_2_2"/><i><font color="Green" title="E12">A6</font></i>: 
( <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattice3.html#NK17" title="LATTICE3:NK.17">"\/"</a> <font color="Maroon" title="c9">Y1</font> &amp; <font color="Maroon" title="c9">Y1</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">X</font> )
 ;<br/>
<a NAME="E4:20_2_2"/>
<font color="Maroon" title="c9">Y1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">X0</font> where <font color="Olive" title="b1">X0</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> : <font color="Olive" title="b1">X0</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">X</font> </span>}</span> 
 
<b>by </b><i><a class="txt" href="#E3:20_2_2"><i><font color="Green" title="E12">A6</font></i></a></i>;<br/>
<b>hence </b><a NAME="E5:20_2_2"/>
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="lattice3.html#NK17" title="LATTICE3:NK.17">"\/"</a> <font color="Olive" title="b1">Y</font></span>)</span> where <font color="Olive" title="b1">Y</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> : <font color="Olive" title="b1">Y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b2">X0</font> where <font color="Olive" title="b2">X0</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> : <font color="Olive" title="b2">X0</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">X</font> </span>}</span>  </span>}</span> 
 <b>by </b><i><a class="txt" href="#E3:20_2_2"><i><font color="Green" title="E12">A6</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>


</div><b>end;</b></div>
<a NAME="E4:20"/>
<font color="Maroon" title="c3">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">X0</font> where <font color="Olive" title="b1">X0</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> : <font color="Olive" title="b1">X0</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">X</font> </span>}</span> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_3"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:20_3"/>
<font color="Maroon" title="c3">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">X0</font> where <font color="Olive" title="b1">X0</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> : <font color="Olive" title="b1">X0</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">X</font> </span>}</span> 
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">X0</font> where <font color="Olive" title="b1">X0</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> : <font color="Olive" title="b1">X0</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">X</font> </span>}</span>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">X</font></span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_3_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c8">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">X</font> or <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">X0</font> where <font color="Olive" title="b1">X0</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> : <font color="Olive" title="b1">X0</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">X</font> </span>}</span>  )</span><br/>

<b>assume </b><a NAME="E1:20_3_1"/><i><font color="Green" title="E12">A7</font></i>: 
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">X</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">X0</font> where <font color="Olive" title="b1">X0</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> : <font color="Olive" title="b1">X0</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">X</font> </span>}</span> </span><br/>

<b>then reconsider </b><font color="Maroon" title="c9">x'</font> = <font color="Maroon" title="c8">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K6" title="MSUALG_5:func.6">CongrLatt</a> <font color="Maroon" title="c2">A</font></span>)</span> ;<br/>
<a NAME="E3:20_3_1"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K6" title="MSUALG_5:func.6">CongrLatt</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span>
 
<b>by </b><i><a class="ref" href="nat_lat.html#D16" title="NAT_LAT:def.16">NAT_LAT:def 16</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c10">x'</font> = <font color="Maroon" title="c9">x'</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> <b>by </b><i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/>
<a NAME="E5:20_3_1"/><i><font color="Green" title="E13">A8</font></i>: 
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c8">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E6:20_3_1"/>
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c10">x'</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">X</font>
 
<b>by </b><i><a class="txt" href="#E1:20_3_1"><i><font color="Green" title="E12">A7</font></i></a>, <a class="ref" href="subset_1.html#T63" title="SUBSET_1:th.63">SUBSET_1:63</a></i>;<br/>
<a NAME="E7:20_3_1"/><b>then </b>
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c10">x'</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">X0</font> where <font color="Olive" title="b1">X0</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> : <font color="Olive" title="b1">X0</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">X</font> </span>}</span> 
 
;<br/>
<b>hence </b><a NAME="E8:20_3_1"/>
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">X0</font> where <font color="Olive" title="b1">X0</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> : <font color="Olive" title="b1">X0</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">X</font> </span>}</span> 
 <b>by </b><i><a class="txt" href="#E5:20_3_1"><i><font color="Green" title="E13">A8</font></i></a>, <a class="ref" href="tarski.html#D4" title="TARSKI:def.4">TARSKI:def 4</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E2:20_3"/>
 <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">X0</font> where <font color="Olive" title="b1">X0</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> : <font color="Olive" title="b1">X0</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">X</font> </span>}</span>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">X</font>
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_3_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c8">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">X0</font> where <font color="Olive" title="b1">X0</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> : <font color="Olive" title="b1">X0</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">X</font> </span>}</span>  or <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">X</font> )</span><br/>

<b>assume </b><a NAME="E1:20_3_2"/>
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">X0</font> where <font color="Olive" title="b1">X0</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> : <font color="Olive" title="b1">X0</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">X</font> </span>}</span> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">X</font></span><br/>

<b>then consider </b><font color="Maroon" title="c9">Y1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:20_3_2"/><i><font color="Green" title="E12">A9</font></i>: 
( <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">Y1</font> &amp; <font color="Maroon" title="c9">Y1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">X0</font> where <font color="Olive" title="b1">X0</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> : <font color="Olive" title="b1">X0</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">X</font> </span>}</span>  )
 <b>by </b><i><a class="ref" href="tarski.html#D4" title="TARSKI:def.4">TARSKI:def 4</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c10">Y2</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span><b> such that </b><br/><a NAME="E5:20_3_2"/><i><font color="Green" title="E13">A10</font></i>: 
( <font color="Maroon" title="c9">Y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">Y2</font> &amp; <font color="Maroon" title="c10">Y2</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">X</font> )
 <b>by </b><i><a class="txt" href="#E3:20_3_2"><i><font color="Green" title="E12">A9</font></i></a></i>;<br/>
<b>thus </b><a NAME="E6:20_3_2"/>
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">X</font>
 <b>by </b><i><a class="txt" href="#E3:20_3_2"><i><font color="Green" title="E12">A9</font></i></a>, <a class="txt" href="#E5:20_3_2"><i><font color="Green" title="E13">A10</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>


</div><b>end;</b></div>
<b>hence </b><a NAME="E5:20"/>
 <a href="lattice3.html#K15" title="LATTICE3:func.15">"\/"</a> <font color="Maroon" title="c3">X</font>,<span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattice3.html#K15" title="LATTICE3:func.15">"\/"</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="lattice3.html#K15" title="LATTICE3:func.15">"\/"</a> <font color="Olive" title="b1">X0</font>,<span class="p3">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span></span>)</span> where <font color="Olive" title="b1">X0</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span> : <font color="Olive" title="b1">X0</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">X</font> </span>}</span> ,<span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">A</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E2:20"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="#E3:20"><i><font color="Green" title="E11">A3</font></i></a>, <a class="ref" href="lattice3.html#T49" title="LATTICE3:th.49">LATTICE3:49</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
