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<b>let </b><font color="Maroon" title="c1">C</font> be  <a href="abcmiz_1.html#V3" title="ABCMIZ_1:attr.3">initialized</a> <a href="abcmiz_1.html#NM5" title="ABCMIZ_1:NM.5">ConstructorSignature</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">s1</font>, <font color="Olive" title="b2">s2</font> being  <a href="msualg_1.html#NM1" title="MSUALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c1">C</font>  st <font color="Olive" title="b1">s1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">s2</font> holds <br/>for <font color="Olive" title="b3">t1</font> being   <a href="abcmiz_1.html#M1" title="ABCMIZ_1:mode.1">expression</a> of <font color="Maroon" title="c1">C</font>,<font color="Olive" title="b1">s1</font><br/> for <font color="Olive" title="b4">t2</font> being   <a href="abcmiz_1.html#M1" title="ABCMIZ_1:mode.1">expression</a> of <font color="Maroon" title="c1">C</font>,<font color="Olive" title="b2">s2</font>  holds <font color="Olive" title="b3">t1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">t2</font></span><br/>

<b>set </b><font color="Maroon" title="c2">X</font> =  <a href="abcmiz_1.html#K28" title="ABCMIZ_1:func.28">MSVars</a> <font color="Maroon" title="c1">C</font>;<br/>
<b>set </b><font color="Maroon" title="c3">Y</font> = <span class="p1">(<span class="default"><a href="abcmiz_1.html#K28" title="ABCMIZ_1:func.28">MSVars</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <span class="p1">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span>;<br/>
<b>consider </b><font color="Maroon" title="c4">A</font> being   <a href="msualg_2.html#NM1" title="MSUALG_2:NM.1">MSSubset</a> of <span class="p1">(<span class="default"><a href="msafree.html#K11" title="MSAFREE:func.11">FreeMSA</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="abcmiz_1.html#K28" title="ABCMIZ_1:func.28">MSVars</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <span class="p3">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span></span>)</span></span>)</span><b> such that </b><br/><a NAME="E2:100"/><i><font color="Green" title="E52">A1</font></i>: 
(  <a href="msafree3.html#K1" title="MSAFREE3:func.1">Free</a> <font color="Maroon" title="c1">C</font>,<span class="p1">(<span class="default"><a href="abcmiz_1.html#K28" title="ABCMIZ_1:func.28">MSVars</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_2.html#K12" title="MSUALG_2:func.12">GenMSAlg</a> <font color="Maroon" title="c4">A</font> &amp; <font color="Maroon" title="c4">A</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <span class="p1">(<span class="default"><a href="msafree.html#K15" title="MSAFREE:func.15">Reverse</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="abcmiz_1.html#K28" title="ABCMIZ_1:func.28">MSVars</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <span class="p3">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span></span>)</span></span>)</span> <a href="equation.html#K1" title="EQUATION:func.1">""</a> <span class="p1">(<span class="default"><a href="abcmiz_1.html#K28" title="ABCMIZ_1:func.28">MSVars</a> <font color="Maroon" title="c1">C</font></span>)</span> )
 <b>by </b><i><a class="ref" href="msafree3.html#D2" title="MSAFREE3:def.2">MSAFREE3:def 2</a></i>;<br/>
<b>let </b><font color="Maroon" title="c5">s1</font>, <font color="Maroon" title="c6">s2</font> be   <a href="msualg_1.html#NM1" title="MSUALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c1">C</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">s1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">s2</font> implies for <font color="Olive" title="b1">t1</font> being   <a href="abcmiz_1.html#M1" title="ABCMIZ_1:mode.1">expression</a> of <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c5">s1</font><br/> for <font color="Olive" title="b2">t2</font> being   <a href="abcmiz_1.html#M1" title="ABCMIZ_1:mode.1">expression</a> of <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c6">s2</font>  holds <font color="Olive" title="b1">t1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">t2</font> )</span><br/>

<a NAME="E3:100"/>
the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><a href="msafree3.html#K1" title="MSAFREE3:func.1">Free</a> <font color="Maroon" title="c1">C</font>,<span class="p2">(<span class="default"><a href="abcmiz_1.html#K28" title="ABCMIZ_1:func.28">MSVars</a> <font color="Maroon" title="c1">C</font></span>)</span></span>)</span> is   <a href="msualg_2.html#NM1" title="MSUALG_2:NM.1">MSSubset</a> of <span class="p1">(<span class="default"><a href="msafree.html#K11" title="MSAFREE:func.11">FreeMSA</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="abcmiz_1.html#K28" title="ABCMIZ_1:func.28">MSVars</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <span class="p3">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="abcmiz_1.html#E2:100"><i><font color="Green" title="E52">A1</font></i></a>, <a class="ref" href="msualg_2.html#D10" title="MSUALG_2:def.10">MSUALG_2:def 10</a></i>;<br/>
<a NAME="E4:100"/><b>then </b>
the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><a href="msafree3.html#K1" title="MSAFREE3:func.1">Free</a> <font color="Maroon" title="c1">C</font>,<span class="p2">(<span class="default"><a href="abcmiz_1.html#K28" title="ABCMIZ_1:func.28">MSVars</a> <font color="Maroon" title="c1">C</font></span>)</span></span>)</span> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><a href="msafree.html#K11" title="MSAFREE:func.11">FreeMSA</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="abcmiz_1.html#K28" title="ABCMIZ_1:func.28">MSVars</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <span class="p3">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="pboole.html#D23" title="PBOOLE:def.23">PBOOLE:def 23</a></i>;<br/>
<a NAME="E5:100"/><b>then </b><i><font color="Green" title="E53">A2</font></i>: 
( the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><a href="msafree3.html#K1" title="MSAFREE3:func.1">Free</a> <font color="Maroon" title="c1">C</font>,<span class="p2">(<span class="default"><a href="abcmiz_1.html#K28" title="ABCMIZ_1:func.28">MSVars</a> <font color="Maroon" title="c1">C</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">s1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><a href="msafree.html#K11" title="MSAFREE:func.11">FreeMSA</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="abcmiz_1.html#K28" title="ABCMIZ_1:func.28">MSVars</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <span class="p3">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">s1</font> &amp; the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><a href="msafree3.html#K1" title="MSAFREE3:func.1">Free</a> <font color="Maroon" title="c1">C</font>,<span class="p2">(<span class="default"><a href="abcmiz_1.html#K28" title="ABCMIZ_1:func.28">MSVars</a> <font color="Maroon" title="c1">C</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">s2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><a href="msafree.html#K11" title="MSAFREE:func.11">FreeMSA</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="abcmiz_1.html#K28" title="ABCMIZ_1:func.28">MSVars</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <span class="p3">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">s2</font> )
 
<b>by </b><i><a class="ref" href="pboole.html#D5" title="PBOOLE:def.5">PBOOLE:def 5</a></i>;<br/>
<b>assume </b><a NAME="E6:100"/>
<font color="Maroon" title="c5">s1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">s2</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">t1</font> being   <a href="abcmiz_1.html#M1" title="ABCMIZ_1:mode.1">expression</a> of <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c5">s1</font><br/> for <font color="Olive" title="b2">t2</font> being   <a href="abcmiz_1.html#M1" title="ABCMIZ_1:mode.1">expression</a> of <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c6">s2</font>  holds <font color="Olive" title="b1">t1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">t2</font></span><br/>

<a NAME="E7:100"/><b>then </b><i><font color="Green" title="E54">A3</font></i>: 
the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><a href="msafree.html#K11" title="MSAFREE:func.11">FreeMSA</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="abcmiz_1.html#K28" title="ABCMIZ_1:func.28">MSVars</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <span class="p3">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">s1</font> <a href="subset_1.html#R1" title="SUBSET_1:pred.1">misses</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><a href="msafree.html#K11" title="MSAFREE:func.11">FreeMSA</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="abcmiz_1.html#K28" title="ABCMIZ_1:func.28">MSVars</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <span class="p3">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">s2</font>
 
<b>by </b><i><a class="ref" href="prob_2.html#D3" title="PROB_2:def.3">PROB_2:def 3</a></i>;<br/>
<b>let </b><font color="Maroon" title="c7">t1</font> be    <a href="abcmiz_1.html#M1" title="ABCMIZ_1:mode.1">expression</a> of <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c5">s1</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">t2</font> being   <a href="abcmiz_1.html#M1" title="ABCMIZ_1:mode.1">expression</a> of <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c6">s2</font>  holds <font color="Maroon" title="c7">t1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">t2</font></span><br/><b>let </b><font color="Maroon" title="c8">t2</font> be    <a href="abcmiz_1.html#M1" title="ABCMIZ_1:mode.1">expression</a> of <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c6">s2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c7">t1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">t2</font></span><br/>



<a NAME="E8:100"/>
( <font color="Maroon" title="c7">t1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><a href="msafree3.html#K1" title="MSAFREE3:func.1">Free</a> <font color="Maroon" title="c1">C</font>,<span class="p2">(<span class="default"><a href="abcmiz_1.html#K28" title="ABCMIZ_1:func.28">MSVars</a> <font color="Maroon" title="c1">C</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">s1</font> &amp; <font color="Maroon" title="c8">t2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><a href="msafree3.html#K1" title="MSAFREE3:func.1">Free</a> <font color="Maroon" title="c1">C</font>,<span class="p2">(<span class="default"><a href="abcmiz_1.html#K28" title="ABCMIZ_1:func.28">MSVars</a> <font color="Maroon" title="c1">C</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">s2</font> )
 
<b>by </b><i><a class="ref" href="abcmiz_1.html#D28" target="_self" title="ABCMIZ_1:def.28">ELEMENT</a></i>;<br/>
<b>hence </b><a NAME="E9:100"/>
<font color="Maroon" title="c7">t1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">t2</font>
 <b>by </b><i><a class="txt" href="abcmiz_1.html#E5:100"><i><font color="Green" title="E53">A2</font></i></a>, <a class="txt" href="abcmiz_1.html#E7:100"><i><font color="Green" title="E54">A3</font></i></a>, <a class="ref" href="xboole_0.html#T3" title="XBOOLE_0:th.3">XBOOLE_0:3</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>
