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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">q</font> being <a href="abcmiz_1.html#V9" title="ABCMIZ_1:attr.9">pure</a>  <a href="abcmiz_1.html#M1" title="ABCMIZ_1:mode.1">expression</a> of <font color="Maroon" title="c1">C</font>, <a href="abcmiz_1.html#K12" title="ABCMIZ_1:func.12">a_Type</a> <font color="Maroon" title="c1">C</font><br/> for <font color="Olive" title="b2">A</font> being <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 <span class="p1">(<span class="default"><a href="abcmiz_1.html#K38" title="ABCMIZ_1:func.38">QuasiAdjs</a> <font color="Maroon" title="c1">C</font></span>)</span> holds   <a href="abcmiz_1.html#K47" title="ABCMIZ_1:func.47">variables_in</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">A</font> <a href="abcmiz_1.html#K40" title="ABCMIZ_1:func.40">ast</a> <font color="Olive" title="b1">q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p2">{<span class="default"> <span class="p3">(<span class="default"><a href="abcmiz_1.html#K45" title="ABCMIZ_1:func.45">variables_in</a> <font color="Olive" title="b3">a</font></span>)</span> where <font color="Olive" title="b3">a</font> is   <a href="abcmiz_1.html#NM10" title="ABCMIZ_1:NM.10">quasi-adjective</a> of <font color="Maroon" title="c1">C</font> : <font color="Olive" title="b3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">A</font> </span>}</span> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="abcmiz_1.html#K45" title="ABCMIZ_1:func.45">variables_in</a> <font color="Olive" title="b1">q</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">q</font> be  <a href="abcmiz_1.html#V9" title="ABCMIZ_1:attr.9">pure</a>  <a href="abcmiz_1.html#M1" title="ABCMIZ_1:mode.1">expression</a> of <font color="Maroon" title="c1">C</font>, <a href="abcmiz_1.html#K12" title="ABCMIZ_1:func.12">a_Type</a> <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"> for <font color="Olive" title="b1">A</font> being <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 <span class="p1">(<span class="default"><a href="abcmiz_1.html#K38" title="ABCMIZ_1:func.38">QuasiAdjs</a> <font color="Maroon" title="c1">C</font></span>)</span> holds   <a href="abcmiz_1.html#K47" title="ABCMIZ_1:func.47">variables_in</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">A</font> <a href="abcmiz_1.html#K40" title="ABCMIZ_1:func.40">ast</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p2">{<span class="default"> <span class="p3">(<span class="default"><a href="abcmiz_1.html#K45" title="ABCMIZ_1:func.45">variables_in</a> <font color="Olive" title="b2">a</font></span>)</span> where <font color="Olive" title="b2">a</font> is   <a href="abcmiz_1.html#NM10" title="ABCMIZ_1:NM.10">quasi-adjective</a> of <font color="Maroon" title="c1">C</font> : <font color="Olive" title="b2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">A</font> </span>}</span> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="abcmiz_1.html#K45" title="ABCMIZ_1:func.45">variables_in</a> <font color="Maroon" title="c2">q</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c3">A</font> be  <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 <span class="p1">(<span class="default"><a href="abcmiz_1.html#K38" title="ABCMIZ_1:func.38">QuasiAdjs</a> <font color="Maroon" title="c1">C</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="abcmiz_1.html#K47" title="ABCMIZ_1:func.47">variables_in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="abcmiz_1.html#K40" title="ABCMIZ_1:func.40">ast</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p2">{<span class="default"> <span class="p3">(<span class="default"><a href="abcmiz_1.html#K45" title="ABCMIZ_1:func.45">variables_in</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is   <a href="abcmiz_1.html#NM10" title="ABCMIZ_1:NM.10">quasi-adjective</a> of <font color="Maroon" title="c1">C</font> : <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> </span>}</span> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="abcmiz_1.html#K45" title="ABCMIZ_1:func.45">variables_in</a> <font color="Maroon" title="c2">q</font></span>)</span></span><br/>





<b>set </b><font color="Maroon" title="c4">X</font> = <span class="p1">(<span class="default"><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 class="p2">(<span class="default"><a href="abcmiz_1.html#K14" title="ABCMIZ_1:func.14">a_Term</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="abcmiz_1.html#K44" title="ABCMIZ_1:func.44">variables_in</a> </span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c3">A</font>;<br/>
<b>set </b><font color="Maroon" title="c5">Y</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="abcmiz_1.html#K45" title="ABCMIZ_1:func.45">variables_in</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is   <a href="abcmiz_1.html#NM10" title="ABCMIZ_1:NM.10">quasi-adjective</a> of <font color="Maroon" title="c1">C</font> : <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> </span>}</span> ;<br/>
<a NAME="E1:188"/><i><font color="Green" title="E92">A1</font></i>: 
<span class="p1">(<span class="default"><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 class="p2">(<span class="default"><a href="abcmiz_1.html#K14" title="ABCMIZ_1:func.14">a_Term</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="abcmiz_1.html#K44" title="ABCMIZ_1:func.44">variables_in</a> </span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c3">A</font> <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="abcmiz_1.html#K45" title="ABCMIZ_1:func.45">variables_in</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is   <a href="abcmiz_1.html#NM10" title="ABCMIZ_1:NM.10">quasi-adjective</a> of <font color="Maroon" title="c1">C</font> : <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> </span>}</span> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="188_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c6">z</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="c6">z</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="abcmiz_1.html#K28" title="ABCMIZ_1:func.28">MSVars</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="abcmiz_1.html#K14" title="ABCMIZ_1:func.14">a_Term</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="abcmiz_1.html#K44" title="ABCMIZ_1:func.44">variables_in</a> </span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c3">A</font> or <font color="Maroon" title="c6">z</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="abcmiz_1.html#K45" title="ABCMIZ_1:func.45">variables_in</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is   <a href="abcmiz_1.html#NM10" title="ABCMIZ_1:NM.10">quasi-adjective</a> of <font color="Maroon" title="c1">C</font> : <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> </span>}</span>  )</span><br/>

<b>assume </b><a NAME="E1:188_1"/>
<font color="Maroon" title="c6">z</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="abcmiz_1.html#K28" title="ABCMIZ_1:func.28">MSVars</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="abcmiz_1.html#K14" title="ABCMIZ_1:func.14">a_Term</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="abcmiz_1.html#K44" title="ABCMIZ_1:func.44">variables_in</a> </span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c3">A</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c6">z</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="abcmiz_1.html#K45" title="ABCMIZ_1:func.45">variables_in</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is   <a href="abcmiz_1.html#NM10" title="ABCMIZ_1:NM.10">quasi-adjective</a> of <font color="Maroon" title="c1">C</font> : <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> </span>}</span> </span><br/>

<b>then consider </b><font color="Maroon" title="c7">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:188_1"/><i><font color="Green" title="E93">B1</font></i>: 
( <font color="Maroon" title="c7">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><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 class="p2">(<span class="default"><a href="abcmiz_1.html#K14" title="ABCMIZ_1:func.14">a_Term</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="abcmiz_1.html#K44" title="ABCMIZ_1:func.44">variables_in</a> </span>)</span> &amp; <font color="Maroon" title="c7">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> &amp; <font color="Maroon" title="c6">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><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 class="p2">(<span class="default"><a href="abcmiz_1.html#K14" title="ABCMIZ_1:func.14">a_Term</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="abcmiz_1.html#K44" title="ABCMIZ_1:func.44">variables_in</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">a</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D12" title="FUNCT_1:def.12">FUNCT_1:def 12</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c8">a</font> = <font color="Maroon" title="c7">a</font> as   <a href="abcmiz_1.html#NM10" title="ABCMIZ_1:NM.10">quasi-adjective</a> of <font color="Maroon" title="c1">C</font> <b>by </b><i><a class="txt" href="abcmiz_1.html#E3:188_1"><i><font color="Green" title="E93">B1</font></i></a>, <a class="ref" href="abcmiz_1.html#T63" target="_self" title="ABCMIZ_1:th.63">Th52</a></i>;<br/>
<a NAME="E5:188_1"/>
<font color="Maroon" title="c6">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="abcmiz_1.html#K45" title="ABCMIZ_1:func.45">variables_in</a> <font color="Maroon" title="c8">a</font>
 
<b>by </b><i><a class="txt" href="abcmiz_1.html#E3:188_1"><i><font color="Green" title="E93">B1</font></i></a>, <a class="ref" href="abcmiz_1.html#D45" target="_self" title="ABCMIZ_1:def.45">VARS'INF</a></i>;<br/>
<b>hence </b><a NAME="E6:188_1"/>
<font color="Maroon" title="c6">z</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="abcmiz_1.html#K45" title="ABCMIZ_1:func.45">variables_in</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is   <a href="abcmiz_1.html#NM10" title="ABCMIZ_1:NM.10">quasi-adjective</a> of <font color="Maroon" title="c1">C</font> : <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> </span>}</span> 
 <b>by </b><i><a class="txt" href="abcmiz_1.html#E3:188_1"><i><font color="Green" title="E93">B1</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="E2:188"/><i><font color="Green" title="E93">A2</font></i>: 
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="abcmiz_1.html#K45" title="ABCMIZ_1:func.45">variables_in</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is   <a href="abcmiz_1.html#NM10" title="ABCMIZ_1:NM.10">quasi-adjective</a> of <font color="Maroon" title="c1">C</font> : <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</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="abcmiz_1.html#K28" title="ABCMIZ_1:func.28">MSVars</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="abcmiz_1.html#K14" title="ABCMIZ_1:func.14">a_Term</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="abcmiz_1.html#K44" title="ABCMIZ_1:func.44">variables_in</a> </span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c3">A</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="188_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c6">z</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="c6">z</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="abcmiz_1.html#K45" title="ABCMIZ_1:func.45">variables_in</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is   <a href="abcmiz_1.html#NM10" title="ABCMIZ_1:NM.10">quasi-adjective</a> of <font color="Maroon" title="c1">C</font> : <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> </span>}</span>  or <font color="Maroon" title="c6">z</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="abcmiz_1.html#K28" title="ABCMIZ_1:func.28">MSVars</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="abcmiz_1.html#K14" title="ABCMIZ_1:func.14">a_Term</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="abcmiz_1.html#K44" title="ABCMIZ_1:func.44">variables_in</a> </span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c3">A</font> )</span><br/>

<b>assume </b><a NAME="E1:188_2"/>
<font color="Maroon" title="c6">z</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="abcmiz_1.html#K45" title="ABCMIZ_1:func.45">variables_in</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is   <a href="abcmiz_1.html#NM10" title="ABCMIZ_1:NM.10">quasi-adjective</a> of <font color="Maroon" title="c1">C</font> : <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</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">z</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="abcmiz_1.html#K28" title="ABCMIZ_1:func.28">MSVars</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="abcmiz_1.html#K14" title="ABCMIZ_1:func.14">a_Term</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="abcmiz_1.html#K44" title="ABCMIZ_1:func.44">variables_in</a> </span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c3">A</font></span><br/>

<b>then consider </b><font color="Maroon" title="c7">a</font> being   <a href="abcmiz_1.html#NM10" title="ABCMIZ_1:NM.10">quasi-adjective</a> of <font color="Maroon" title="c1">C</font><b> such that </b><br/><a NAME="E3:188_2"/><i><font color="Green" title="E94">B2</font></i>: 
( <font color="Maroon" title="c6">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="abcmiz_1.html#K45" title="ABCMIZ_1:func.45">variables_in</a> <font color="Maroon" title="c7">a</font> &amp; <font color="Maroon" title="c7">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> )
 ;<br/>
<a NAME="E4:188_2"/>
( <font color="Maroon" title="c6">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><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 class="p2">(<span class="default"><a href="abcmiz_1.html#K14" title="ABCMIZ_1:func.14">a_Term</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="abcmiz_1.html#K44" title="ABCMIZ_1:func.44">variables_in</a> </span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">a</font> &amp;  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><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 class="p2">(<span class="default"><a href="abcmiz_1.html#K14" title="ABCMIZ_1:func.14">a_Term</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="abcmiz_1.html#K44" title="ABCMIZ_1:func.44">variables_in</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_3.html#K3" title="CARD_3:func.3">Union</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> )
 
<b>by </b><i><a class="txt" href="abcmiz_1.html#E3:188_2"><i><font color="Green" title="E94">B2</font></i></a>, <a class="ref" href="abcmiz_1.html#D45" target="_self" title="ABCMIZ_1:def.45">VARS'INF</a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<b>hence </b><a NAME="E5:188_2"/>
<font color="Maroon" title="c6">z</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="abcmiz_1.html#K28" title="ABCMIZ_1:func.28">MSVars</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="abcmiz_1.html#K14" title="ABCMIZ_1:func.14">a_Term</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="abcmiz_1.html#K44" title="ABCMIZ_1:func.44">variables_in</a> </span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c3">A</font>
 <b>by </b><i><a class="txt" href="abcmiz_1.html#E3:188_2"><i><font color="Green" title="E94">B2</font></i></a>, <a class="ref" href="funct_1.html#D12" title="FUNCT_1:def.12">FUNCT_1:def 12</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 href="abcmiz_1.html#K47" title="ABCMIZ_1:func.47">variables_in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="abcmiz_1.html#K40" title="ABCMIZ_1:func.40">ast</a> <font color="Maroon" title="c2">q</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<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 class="p4">(<span class="default"><a href="abcmiz_1.html#K14" title="ABCMIZ_1:func.14">a_Term</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="abcmiz_1.html#K44" title="ABCMIZ_1:func.44">variables_in</a> </span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <span class="p3">(<span class="default"><a href="abcmiz_1.html#K41" title="ABCMIZ_1:func.41">adjs</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="abcmiz_1.html#K40" title="ABCMIZ_1:func.40">ast</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="abcmiz_1.html#K45" title="ABCMIZ_1:func.45">variables_in</a> <font color="Maroon" title="c2">q</font></span>)</span>
<b>by </b><i><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<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 class="p4">(<span class="default"><a href="abcmiz_1.html#K14" title="ABCMIZ_1:func.14">a_Term</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="abcmiz_1.html#K44" title="ABCMIZ_1:func.44">variables_in</a> </span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c3">A</font></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="abcmiz_1.html#K45" title="ABCMIZ_1:func.45">variables_in</a> <font color="Maroon" title="c2">q</font></span>)</span>
<b>by </b><i><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p2">{<span class="default"> <span class="p3">(<span class="default"><a href="abcmiz_1.html#K45" title="ABCMIZ_1:func.45">variables_in</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is   <a href="abcmiz_1.html#NM10" title="ABCMIZ_1:NM.10">quasi-adjective</a> of <font color="Maroon" title="c1">C</font> : <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> </span>}</span> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="abcmiz_1.html#K45" title="ABCMIZ_1:func.45">variables_in</a> <font color="Maroon" title="c2">q</font></span>)</span>
<b>by </b><i><a class="txt" href="abcmiz_1.html#E1:188"><i><font color="Green" title="E92">A1</font></i></a>, <a class="txt" href="abcmiz_1.html#E2:188"><i><font color="Green" title="E93">A2</font></i></a>, <a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</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>
