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<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">T</font> being   <a href="abcmiz_1.html#M3" title="ABCMIZ_1:mode.3">quasi-type</a> of <font color="Maroon" title="c1">C</font><br/> for <font color="Olive" title="b2">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> 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#K43" title="ABCMIZ_1:func.43">ast</a> <font color="Olive" title="b1">T</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="b2">a</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="abcmiz_1.html#K47" title="ABCMIZ_1:func.47">variables_in</a> <font color="Olive" title="b1">T</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">T</font> be    <a href="abcmiz_1.html#M3" title="ABCMIZ_1:mode.3">quasi-type</a> of <font color="Maroon" title="c1">C</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">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> 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#K43" title="ABCMIZ_1:func.43">ast</a> <font color="Maroon" title="c2">T</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">a</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="abcmiz_1.html#K47" title="ABCMIZ_1:func.47">variables_in</a> <font color="Maroon" title="c2">T</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">a</font> be   <a href="abcmiz_1.html#NM10" title="ABCMIZ_1:NM.10">quasi-adjective</a> of <font color="Maroon" title="c1">C</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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#K43" title="ABCMIZ_1:func.43">ast</a> <font color="Maroon" title="c2">T</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c3">a</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="abcmiz_1.html#K47" title="ABCMIZ_1:func.47">variables_in</a> <font color="Maroon" title="c2">T</font></span>)</span></span><br/>





<a NAME="E1:185"/><span class="lab"><font color="Green" title="E91">A1</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">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#U3" title="MSUALG_1:sel.3">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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<span class="kw">thus </span> <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#K43" title="ABCMIZ_1:func.43">ast</a> <font color="Maroon" title="c2">T</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#K7" title="RELSET_1:func.7">.:</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#K43" title="ABCMIZ_1:func.43">ast</a> <font color="Maroon" title="c2">T</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> <span class="p2">(<span class="default"><a href="abcmiz_1.html#K42" title="ABCMIZ_1:func.42">the_base_of</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></span>
<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#K7" title="RELSET_1:func.7">.:</a> <span class="p3">(<span class="default"><span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">a</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p4">(<span class="default"><a href="abcmiz_1.html#K41" title="ABCMIZ_1:func.41">adjs</a> <font color="Maroon" title="c2">T</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> <span class="p2">(<span class="default"><a href="abcmiz_1.html#K42" title="ABCMIZ_1:func.42">the_base_of</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></span>
<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"><span class="p5">(<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="p5">(<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#K7" title="RELSET_1:func.7">.:</a> <span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">a</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<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="p5">(<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#K7" title="RELSET_1:func.7">.:</a> <span class="p4">(<span class="default"><a href="abcmiz_1.html#K41" title="ABCMIZ_1:func.41">adjs</a> <font color="Maroon" title="c2">T</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> <span class="p2">(<span class="default"><a href="abcmiz_1.html#K42" title="ABCMIZ_1:func.42">the_base_of</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T153" title="RELAT_1:th.153">RELAT_1:153</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<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="p5">(<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#K7" title="RELSET_1:func.7">.:</a> <span class="p4"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">a</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2">(<span class="default"><a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<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="p5">(<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#K7" title="RELSET_1:func.7">.:</a> <span class="p4">(<span class="default"><a href="abcmiz_1.html#K41" title="ABCMIZ_1:func.41">adjs</a> <font color="Maroon" title="c2">T</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> <span class="p2">(<span class="default"><a href="abcmiz_1.html#K42" title="ABCMIZ_1:func.42">the_base_of</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T96" title="ZFMISC_1:th.96">ZFMISC_1:96</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p2">(<span class="default"><a href="relat_1.html#K11" title="RELAT_1:func.11">Im</a> <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>,<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#K47" title="ABCMIZ_1:func.47">variables_in</a> <font color="Maroon" title="c2">T</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T4" title="XBOOLE_1:th.4">XBOOLE_1:4</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<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="p5">(<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="c3">a</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></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#K47" title="ABCMIZ_1:func.47">variables_in</a> <font color="Maroon" title="c2">T</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:185"><span class="lab"><font color="Green" title="E91">A1</font></span></a>, <a class="ref" href="funct_1.html#T117" title="FUNCT_1:th.117">FUNCT_1:117</a></span>
<br/>.= 
<span class="p1">(<span class="default"><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>,<span class="p3">(<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="c3">a</font></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#K47" title="ABCMIZ_1:func.47">variables_in</a> <font color="Maroon" title="c2">T</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T31" title="ZFMISC_1:th.31">ZFMISC_1:31</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="abcmiz_1.html#K45" title="ABCMIZ_1:func.45">variables_in</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="abcmiz_1.html#K47" title="ABCMIZ_1:func.47">variables_in</a> <font color="Maroon" title="c2">T</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="abcmiz_1.html#D45" target="_self" title="ABCMIZ_1:def.45">Def45</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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