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<span class="kw">let </span><font color="Maroon" title="c2">X</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 <a href="abcmiz_1.html#K2" title="ABCMIZ_1:func.2">Vars</a> ; <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#K1" title="ABCMIZ_1:func.1">varcl</a> <font color="Maroon" title="c2">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">X</font> implies for <font color="Olive" title="b1">s</font> being  <a href="msualg_1.html#NM1" title="MSUALG_1:NM.1">SortSymbol</a> of <a href="abcmiz_1.html#K27" title="ABCMIZ_1:func.27">MaxConstrSign</a>   ex <font color="Olive" title="b2">m</font> being  <a href="abcmiz_1.html#V2" title="ABCMIZ_1:attr.2">constructor</a>   <a href="abcmiz_1.html#M2" title="ABCMIZ_1:mode.2">OperSymbol</a> of <font color="Olive" title="b1">s</font> ex <font color="Olive" title="b3">p</font> being   <a href="trees_4.html#M1" title="TREES_4:mode.1">FinSequence</a> of  <a href="abcmiz_1.html#K34" title="ABCMIZ_1:func.34">QuasiTerms</a> <a href="abcmiz_1.html#K27" title="ABCMIZ_1:func.27">MaxConstrSign</a>  st <br/>(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b3">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Olive" title="b2">m</font></span>)</span> &amp;  <a href="abcmiz_1.html#K46" title="ABCMIZ_1:func.46">vars</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">m</font> <a href="abcmiz_1.html#K36" title="ABCMIZ_1:func.36">-trm</a> <font color="Olive" title="b3">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">X</font> ) )</span><br/>

<span class="kw">assume </span><a NAME="E1:105"/><span class="lab"><font color="Green" title="E43">Z0</font></span>: 
 <a href="abcmiz_1.html#K1" title="ABCMIZ_1:func.1">varcl</a> <font color="Maroon" title="c2">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">X</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">s</font> being  <a href="msualg_1.html#NM1" title="MSUALG_1:NM.1">SortSymbol</a> of <a href="abcmiz_1.html#K27" title="ABCMIZ_1:func.27">MaxConstrSign</a>   ex <font color="Olive" title="b2">m</font> being  <a href="abcmiz_1.html#V2" title="ABCMIZ_1:attr.2">constructor</a>   <a href="abcmiz_1.html#M2" title="ABCMIZ_1:mode.2">OperSymbol</a> of <font color="Olive" title="b1">s</font> ex <font color="Olive" title="b3">p</font> being   <a href="trees_4.html#M1" title="TREES_4:mode.1">FinSequence</a> of  <a href="abcmiz_1.html#K34" title="ABCMIZ_1:func.34">QuasiTerms</a> <a href="abcmiz_1.html#K27" title="ABCMIZ_1:func.27">MaxConstrSign</a>  st <br/>(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b3">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Olive" title="b2">m</font></span>)</span> &amp;  <a href="abcmiz_1.html#K46" title="ABCMIZ_1:func.46">vars</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">m</font> <a href="abcmiz_1.html#K36" title="ABCMIZ_1:func.36">-trm</a> <font color="Olive" title="b3">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">X</font> )</span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c3">l</font> being   <a href="abcmiz_1.html#NM4" title="ABCMIZ_1:NM.4">quasi-loci</a><span class="kw"> such that </span><br/><a NAME="E3:105"/><span class="lab"><font color="Green" title="E44">A0</font></span>: 
 <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c3">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">X</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="abcmiz_a.html#T31" target="_self" title="ABCMIZ_A:th.31">ThLoci</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">n</font> =  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">l</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">C</font> =  <a href="abcmiz_1.html#K27" title="ABCMIZ_1:func.27">MaxConstrSign</a> ;<br/>
<span class="kw">let </span><font color="Maroon" title="c6">s</font> be   <a href="msualg_1.html#NM1" title="MSUALG_1:NM.1">SortSymbol</a> of <a href="abcmiz_1.html#K27" title="ABCMIZ_1:func.27">MaxConstrSign</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">m</font> being  <a href="abcmiz_1.html#V2" title="ABCMIZ_1:attr.2">constructor</a>   <a href="abcmiz_1.html#M2" title="ABCMIZ_1:mode.2">OperSymbol</a> of <font color="Maroon" title="c6">s</font> ex <font color="Olive" title="b2">p</font> being   <a href="trees_4.html#M1" title="TREES_4:mode.1">FinSequence</a> of  <a href="abcmiz_1.html#K34" title="ABCMIZ_1:func.34">QuasiTerms</a> <a href="abcmiz_1.html#K27" title="ABCMIZ_1:func.27">MaxConstrSign</a>  st <br/>(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Olive" title="b1">m</font></span>)</span> &amp;  <a href="abcmiz_1.html#K46" title="ABCMIZ_1:func.46">vars</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">m</font> <a href="abcmiz_1.html#K36" title="ABCMIZ_1:func.36">-trm</a> <font color="Olive" title="b2">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">X</font> )</span><br/>

<span class="kw">consider </span><font color="Maroon" title="c7">m</font> being   <a href="abcmiz_1.html#V2" title="ABCMIZ_1:attr.2">constructor</a>   <a href="abcmiz_1.html#M2" title="ABCMIZ_1:mode.2">OperSymbol</a> of <font color="Maroon" title="c6">s</font><span class="kw"> such that </span><br/><a NAME="E5:105"/><span class="lab"><font color="Green" title="E45">A1</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c7">m</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">l</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="abcmiz_a.html#T57" target="_self" title="ABCMIZ_A:th.57">Th61</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c7">m</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">p</font> being   <a href="trees_4.html#M1" title="TREES_4:mode.1">FinSequence</a> of  <a href="abcmiz_1.html#K34" title="ABCMIZ_1:func.34">QuasiTerms</a> <a href="abcmiz_1.html#K27" title="ABCMIZ_1:func.27">MaxConstrSign</a>  st <br/>(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c7">m</font></span>)</span> &amp;  <a href="abcmiz_1.html#K46" title="ABCMIZ_1:func.46">vars</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">m</font> <a href="abcmiz_1.html#K36" title="ABCMIZ_1:func.36">-trm</a> <font color="Olive" title="b1">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">X</font> )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c8">p</font> =  <a href="abcmiz_a.html#K16" title="ABCMIZ_A:func.16">args</a> <font color="Maroon" title="c3">l</font>;<br/>
<span class="kw">take </span>
 <a href="abcmiz_a.html#K16" title="ABCMIZ_A:func.16">args</a> <font color="Maroon" title="c3">l</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="abcmiz_a.html#K16" title="ABCMIZ_A:func.16">args</a> <font color="Maroon" title="c3">l</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c7">m</font></span>)</span> &amp;  <a href="abcmiz_1.html#K46" title="ABCMIZ_1:func.46">vars</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">m</font> <a href="abcmiz_1.html#K36" title="ABCMIZ_1:func.36">-trm</a> <span class="p2">(<span class="default"><a href="abcmiz_a.html#K16" title="ABCMIZ_A:func.16">args</a> <font color="Maroon" title="c3">l</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">X</font> )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c9">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">t</font></span>)</span> where <font color="Olive" title="b1">t</font> is   <a href="abcmiz_1.html#NM9" title="ABCMIZ_1:NM.9">quasi-term</a> of <a href="abcmiz_1.html#K27" title="ABCMIZ_1:func.27">MaxConstrSign</a>  : <font color="Olive" title="b1">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="abcmiz_a.html#K16" title="ABCMIZ_A:func.16">args</a> <font color="Maroon" title="c3">l</font></span>)</span> </span>}</span> ;<br/>
<span class="kw">thus </span><a NAME="E6:105"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="abcmiz_a.html#K16" title="ABCMIZ_A:func.16">args</a> <font color="Maroon" title="c3">l</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c7">m</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:105"><span class="lab"><font color="Green" title="E45">A1</font></span></a>, <a class="ref" href="abcmiz_a.html#D18" target="_self" title="ABCMIZ_A:def.18">ARGSL</a></span>; <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#K46" title="ABCMIZ_1:func.46">vars</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">m</font> <a href="abcmiz_1.html#K36" title="ABCMIZ_1:func.36">-trm</a> <span class="p2">(<span class="default"><a href="abcmiz_a.html#K16" title="ABCMIZ_A:func.16">args</a> <font color="Maroon" title="c3">l</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">X</font></span><br/>

<span class="kw">thus </span><a NAME="E7:105"/>
 <a href="abcmiz_1.html#K46" title="ABCMIZ_1:func.46">vars</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">m</font> <a href="abcmiz_1.html#K36" title="ABCMIZ_1:func.36">-trm</a> <span class="p2">(<span class="default"><a href="abcmiz_a.html#K16" title="ABCMIZ_A:func.16">args</a> <font color="Maroon" title="c3">l</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">X</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:105"><span class="lab"><font color="Green" title="E43">Z0</font></span></a>, <a class="txt" href="#E3:105"><span class="lab"><font color="Green" title="E44">A0</font></span></a>, <a class="txt" href="#E5:105"><span class="lab"><font color="Green" title="E45">A1</font></span></a>, <a class="ref" href="abcmiz_a.html#T58" target="_self" title="ABCMIZ_A:th.58">Th63</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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