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<span class="kw">let </span><font color="Maroon" title="c2">l</font> be   <a href="abcmiz_1.html#NM4" title="ABCMIZ_1:NM.4">quasi-loci</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">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> <br/> for <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>  st  <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> <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="c2">l</font> holds <br/> <a href="abcmiz_1.html#K45" title="ABCMIZ_1:func.45">variables_in</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> <span class="p2">(<span class="default"><a href="abcmiz_a.html#K16" title="ABCMIZ_A:func.16">args</a> <font color="Maroon" title="c2">l</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c2">l</font></span><br/>

<span class="kw">set </span><font color="Maroon" title="c3">X</font> =  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c2">l</font>;<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="c2">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"> for <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>  st  <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> <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="c2">l</font> holds <br/> <a href="abcmiz_1.html#K45" title="ABCMIZ_1:func.45">variables_in</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> <span class="p2">(<span class="default"><a href="abcmiz_a.html#K16" title="ABCMIZ_A:func.16">args</a> <font color="Maroon" title="c2">l</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c2">l</font></span><br/><span class="kw">let </span><font color="Maroon" title="c7">m</font> be   <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>; <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="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="c2">l</font> implies  <a href="abcmiz_1.html#K45" title="ABCMIZ_1:func.45">variables_in</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="c2">l</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c2">l</font> )</span><br/>



<span class="kw">assume </span><a NAME="E1:104"/><span class="lab"><font color="Green" title="E42">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="c2">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="abcmiz_1.html#K45" title="ABCMIZ_1:func.45">variables_in</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="c2">l</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c2">l</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="c2">l</font>;<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="c2">l</font></span>)</span> </span>}</span> ;<br/>
<a NAME="E2:104"/><span class="lab"><font color="Green" title="E43">AA</font></span>: 
 <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="c2">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="#E1:104"><span class="lab"><font color="Green" title="E42">A1</font></span></a>, <a class="ref" href="abcmiz_a.html#D18" target="_self" title="ABCMIZ_A:def.18">ARGSL</a></span>;<br/>
<a NAME="E3:104"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A2</font></span>: 
 <a href="abcmiz_1.html#K45" title="ABCMIZ_1:func.45">variables_in</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="c2">l</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</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">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="c2">l</font></span>)</span> </span>}</span> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="abcmiz_1.html#T90" title="ABCMIZ_1:th.90">ABCMIZ_1:90</a></span>;<br/>
<a NAME="E4:104"/><span class="lab"><font color="Green" title="E45">B0</font></span>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="abcmiz_a.html#K16" title="ABCMIZ_A:func.16">args</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">l</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:104"><span class="lab"><font color="Green" title="E42">A1</font></span></a>, <a class="txt" href="#E2:104"><span class="lab"><font color="Green" title="E43">AA</font></span></a>, <a class="ref" href="finseq_3.html#T31" title="FINSEQ_3:th.31">FINSEQ_3:31</a></span>;<br/>
<span class="kw">thus </span><a NAME="E5:104"/>
 <a href="abcmiz_1.html#K45" title="ABCMIZ_1:func.45">variables_in</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="c2">l</font></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c2">l</font>
  <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c2">l</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="abcmiz_1.html#K45" title="ABCMIZ_1:func.45">variables_in</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="c2">l</font></span>)</span></span>)</span></span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="104_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c10">s</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c10">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="abcmiz_1.html#K45" title="ABCMIZ_1:func.45">variables_in</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="c2">l</font></span>)</span></span>)</span> or <font color="Maroon" title="c10">s</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> <font color="Maroon" title="c2">l</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:104_1"/>
<font color="Maroon" title="c10">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="abcmiz_1.html#K45" title="ABCMIZ_1:func.45">variables_in</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="c2">l</font></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c10">s</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> <font color="Maroon" title="c2">l</font></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c11">A</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E3:104_1"/><span class="lab"><font color="Green" title="E46">A3</font></span>: 
( <font color="Maroon" title="c10">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">A</font> &amp; <font color="Maroon" title="c11">A</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">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="c2">l</font></span>)</span> </span>}</span>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:104"><span class="lab"><font color="Green" title="E44">A2</font></span></a>, <a class="ref" href="tarski.html#D4" title="TARSKI:def.4">TARSKI:def 4</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c12">t</font> being   <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> <span class="kw"> such that </span><br/><a NAME="E5:104_1"/><span class="lab"><font color="Green" title="E47">A4</font></span>: 
( <font color="Maroon" title="c11">A</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="c12">t</font> &amp; <font color="Maroon" title="c12">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="c2">l</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:104_1"><span class="lab"><font color="Green" title="E46">A3</font></span></a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c13">z</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E7:104_1"/><span class="lab"><font color="Green" title="E48">A5</font></span>: 
( <font color="Maroon" title="c13">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="abcmiz_a.html#K16" title="ABCMIZ_A:func.16">args</a> <font color="Maroon" title="c2">l</font></span>)</span> &amp; <font color="Maroon" title="c12">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="abcmiz_a.html#K16" title="ABCMIZ_A:func.16">args</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">z</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:104_1"><span class="lab"><font color="Green" title="E47">A4</font></span></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c14">z</font> = <font color="Maroon" title="c13">z</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:104_1"><span class="lab"><font color="Green" title="E48">A5</font></span></a></span>;<br/>
<a NAME="E9:104_1"/>
<font color="Maroon" title="c2">l</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">l</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c14">z</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:104"><span class="lab"><font color="Green" title="E45">B0</font></span></a>, <a class="txt" href="#E7:104_1"><span class="lab"><font color="Green" title="E48">A5</font></span></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></span>;<br/>
<a NAME="E10:104_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E49">A6</font></span>: 
<font color="Maroon" title="c2">l</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c14">z</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> <font color="Maroon" title="c2">l</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:104"><span class="lab"><font color="Green" title="E45">B0</font></span></a>, <a class="txt" href="#E7:104_1"><span class="lab"><font color="Green" title="E48">A5</font></span></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></span>;<br/>
<a NAME="E11:104_1"/>
<span class="p1">(<span class="default"><a href="abcmiz_a.html#K16" title="ABCMIZ_A:func.16">args</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">l</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c14">z</font></span>)</span> <a href="abcmiz_1.html#K35" title="ABCMIZ_1:func.35">-term</a> <a href="abcmiz_1.html#K27" title="ABCMIZ_1:func.27">MaxConstrSign</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:104"><span class="lab"><font color="Green" title="E45">B0</font></span></a>, <a class="txt" href="#E7:104_1"><span class="lab"><font color="Green" title="E48">A5</font></span></a>, <a class="ref" href="abcmiz_a.html#D18" target="_self" title="ABCMIZ_A:def.18">ARGSL</a></span>;<br/>
<a NAME="E12:104_1"/><span class="kw">then </span>
<font color="Maroon" title="c11">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">l</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c14">z</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:104_1"><span class="lab"><font color="Green" title="E47">A4</font></span></a>, <a class="txt" href="#E7:104_1"><span class="lab"><font color="Green" title="E48">A5</font></span></a>, <a class="ref" href="abcmiz_1.html#T86" title="ABCMIZ_1:th.86">ABCMIZ_1:86</a></span>;<br/>
<span class="kw">hence </span><a NAME="E13:104_1"/>
<font color="Maroon" title="c10">s</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> <font color="Maroon" title="c2">l</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:104_1"><span class="lab"><font color="Green" title="E46">A3</font></span></a>, <a class="txt" href="#E10:104_1"><span class="lab"><font color="Green" title="E49">A6</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</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/>


</div><span class="kw">end;</span></div>

<span class="kw">let </span><font color="Maroon" title="c10">s</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c10">s</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> <font color="Maroon" title="c2">l</font> or <font color="Maroon" title="c10">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="abcmiz_1.html#K45" title="ABCMIZ_1:func.45">variables_in</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="c2">l</font></span>)</span></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E6:104"/>
<font color="Maroon" title="c10">s</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> <font color="Maroon" title="c2">l</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c10">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="abcmiz_1.html#K45" title="ABCMIZ_1:func.45">variables_in</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="c2">l</font></span>)</span></span>)</span></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c11">z</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E8:104"/><span class="lab"><font color="Green" title="E46">A7</font></span>: 
( <font color="Maroon" title="c11">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">l</font> &amp; <font color="Maroon" title="c10">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">l</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">z</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c12">z</font> = <font color="Maroon" title="c11">z</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:104"><span class="lab"><font color="Green" title="E46">A7</font></span></a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c13">t</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c2">l</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c12">z</font></span>)</span> <a href="abcmiz_1.html#K35" title="ABCMIZ_1:func.35">-term</a> <a href="abcmiz_1.html#K27" title="ABCMIZ_1:func.27">MaxConstrSign</a> ;<br/>
<a NAME="E10:104"/>
( <span class="p1">(<span class="default"><a href="abcmiz_a.html#K16" title="ABCMIZ_A:func.16">args</a> <font color="Maroon" title="c2">l</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">l</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c12">z</font></span>)</span> <a href="abcmiz_1.html#K35" title="ABCMIZ_1:func.35">-term</a> <a href="abcmiz_1.html#K27" title="ABCMIZ_1:func.27">MaxConstrSign</a>  &amp; <font color="Maroon" title="c2">l</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">l</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c12">z</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:104"><span class="lab"><font color="Green" title="E46">A7</font></span></a>, <a class="ref" href="abcmiz_a.html#D18" target="_self" title="ABCMIZ_A:def.18">ARGSL</a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></span>;<br/>
<a NAME="E11:104"/><span class="kw">then </span>
(  <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"><font color="Maroon" title="c2">l</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c12">z</font></span>)</span> <a href="abcmiz_1.html#K35" title="ABCMIZ_1:func.35">-term</a> <a href="abcmiz_1.html#K27" title="ABCMIZ_1:func.27">MaxConstrSign</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c10">s</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">l</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c12">z</font></span>)</span> <a href="abcmiz_1.html#K35" title="ABCMIZ_1:func.35">-term</a> <a href="abcmiz_1.html#K27" title="ABCMIZ_1:func.27">MaxConstrSign</a>  <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="c2">l</font></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:104"><span class="lab"><font color="Green" title="E45">B0</font></span></a>, <a class="txt" href="#E8:104"><span class="lab"><font color="Green" title="E46">A7</font></span></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a>, <a class="ref" href="abcmiz_1.html#T86" title="ABCMIZ_1:th.86">ABCMIZ_1:86</a></span>;<br/>
<a NAME="E12:104"/><span class="kw">then </span>
( <font color="Maroon" title="c10">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c10">s</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp; <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c10">s</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <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">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="c2">l</font></span>)</span> </span>}</span>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E13:104"/>
<font color="Maroon" title="c10">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="abcmiz_1.html#K45" title="ABCMIZ_1:func.45">variables_in</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="c2">l</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:104"><span class="lab"><font color="Green" title="E44">A2</font></span></a>, <a class="ref" href="tarski.html#D4" title="TARSKI:def.4">TARSKI:def 4</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/>


</div>
