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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">t</font> being   <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="abcmiz_1.html#M1" title="ABCMIZ_1:mode.1">expression</a> of <font color="Maroon" title="c1">C</font>, <a href="abcmiz_1.html#K13" title="ABCMIZ_1:func.13">an_Adj</a> <font color="Maroon" title="c1">C</font> holds   <a href="abcmiz_1.html#K45" title="ABCMIZ_1:func.45">variables_in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="abcmiz_1.html#K33" title="ABCMIZ_1:func.33">ast</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="abcmiz_1.html#K31" title="ABCMIZ_1:func.31">term</a> <font color="Olive" title="b2">a</font>,<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#K45" title="ABCMIZ_1:func.45">variables_in</a> <font color="Olive" title="b1">t</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">t</font> be    <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="abcmiz_1.html#M1" title="ABCMIZ_1:mode.1">expression</a> of <font color="Maroon" title="c1">C</font>, <a href="abcmiz_1.html#K13" title="ABCMIZ_1:func.13">an_Adj</a> <font color="Maroon" title="c1">C</font> holds   <a href="abcmiz_1.html#K45" title="ABCMIZ_1:func.45">variables_in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="abcmiz_1.html#K33" title="ABCMIZ_1:func.33">ast</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="abcmiz_1.html#K31" title="ABCMIZ_1:func.31">term</a> <font color="Olive" title="b1">a</font>,<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#K45" title="ABCMIZ_1:func.45">variables_in</a> <font color="Maroon" title="c2">t</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c3">a</font> be    <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#K13" title="ABCMIZ_1:func.13">an_Adj</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">  <a href="abcmiz_1.html#K45" title="ABCMIZ_1:func.45">variables_in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="abcmiz_1.html#K33" title="ABCMIZ_1:func.33">ast</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="abcmiz_1.html#K31" title="ABCMIZ_1:func.31">term</a> <font color="Maroon" title="c3">a</font>,<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#K45" title="ABCMIZ_1:func.45">variables_in</a> <font color="Maroon" title="c2">t</font></span>)</span></span><br/>





<a NAME="E1:180"/>
<span class="p1">(<span class="default"><a href="abcmiz_1.html#K33" title="ABCMIZ_1:func.33">ast</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="abcmiz_1.html#K31" title="ABCMIZ_1:func.31">term</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="abcmiz_1.html#K9" title="ABCMIZ_1:func.9">*</a> ,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="trees_4.html#K4" title="TREES_4:func.4">-tree</a> <span class="p1"><a href="lang1.html#K4" title="LANG1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">t</font></span><a href="lang1.html#K4" title="LANG1:func.4">*&gt;</a></span>
 
<b>by </b><i><a class="ref" href="abcmiz_1.html#T46" target="_self" title="ABCMIZ_1:th.46">ThAst</a></i>;<br/>
<a NAME="E2:180"/><b>then </b>
 <a href="abcmiz_1.html#K45" title="ABCMIZ_1:func.45">variables_in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="abcmiz_1.html#K33" title="ABCMIZ_1:func.33">ast</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="abcmiz_1.html#K31" title="ABCMIZ_1:func.31">term</a> <font color="Maroon" title="c3">a</font>,<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"><span class="p2">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="msafree3.html#K2" title="MSAFREE3:func.2">variables_in</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="msafree3.html#K2" title="MSAFREE3:func.2">variables_in</a> <font color="Maroon" title="c2">t</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="abcmiz_1.html#K8" title="ABCMIZ_1:func.8">a_Term</a> 
 
<b>by </b><i><a class="ref" href="abcmiz_1.html#T96" target="_self" title="ABCMIZ_1:th.96">Aux2</a></i>;<br/>
<b>hence </b><a NAME="E3:180"/>
 <a href="abcmiz_1.html#K45" title="ABCMIZ_1:func.45">variables_in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="abcmiz_1.html#K33" title="ABCMIZ_1:func.33">ast</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="abcmiz_1.html#K31" title="ABCMIZ_1:func.31">term</a> <font color="Maroon" title="c3">a</font>,<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#K45" title="ABCMIZ_1:func.45">variables_in</a> <font color="Maroon" title="c2">t</font></span>)</span>
 <b>by </b><i><a class="ref" href="pboole.html#D7" title="PBOOLE:def.7">PBOOLE:def 7</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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