<?xml version="1.0"?>
<div class="add">

<span class="kw">set </span><font color="Maroon" title="c2">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="c3">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</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>   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> 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> <font color="Maroon" title="c3">n</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">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="c4">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> <font color="Maroon" title="c3">n</font></span><br/>



<span class="kw">deffunc </span><font color="Maroon">H<sub>1</sub></font>(  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>) <span class="kw">-&gt; </span>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  = <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,$1</span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c5">l</font> being   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a><span class="kw"> such that </span><br/><a NAME="E2:103"/><span class="lab"><font color="Green" title="E41">F0</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">n</font>
 <span class="kw">and </span><br/><a NAME="E3:103"/><span class="lab"><font color="Green" title="E42">F1</font></span>: 
for <font color="Olive" title="b1">i</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">i</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="c5">l</font> holds <br/><font color="Maroon" title="c5">l</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">i</font>)
 <span class="kw">from</span> <span class="lab"><a class="ref" href="finseq_1.html#S2" title="FINSEQ_1:sch.2">FINSEQ_1:sch 2</a>();<br/></span>
<a NAME="E4:103"/><span class="lab"><font color="Green" title="E43">F2</font></span>: 
<font color="Maroon" title="c5">l</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="103_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c6">i</font>, <font color="Maroon" title="c7">j</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="funct_1.html#D8" title="FUNCT_1:def.8">FUNCT_1:def 8</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="c6">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <font color="Maroon" title="c5">l</font> or  not <font color="Maroon" title="c7">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <font color="Maroon" title="c5">l</font> or  not <font color="Maroon" title="c5">l</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">l</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">j</font> or <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">j</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:103_1"/><span class="lab"><font color="Green" title="E44">B1</font></span>: 
( <font color="Maroon" title="c6">i</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="c5">l</font> &amp; <font color="Maroon" title="c7">j</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="c5">l</font> &amp; <font color="Maroon" title="c5">l</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">l</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">j</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="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">j</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c8">i</font> = <font color="Maroon" title="c6">i</font>, <font color="Maroon" title="c9">j</font> = <font color="Maroon" title="c7">j</font> as   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:103_1"><span class="lab"><font color="Green" title="E44">B1</font></span></a></span>;<br/>
<a NAME="E3:103_1"/>
( <font color="Maroon" title="c5">l</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c8">i</font>) &amp; <font color="Maroon" title="c5">l</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c9">j</font>) )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:103"><span class="lab"><font color="Green" title="E42">F1</font></span></a>, <a class="txt" href="#E1:103_1"><span class="lab"><font color="Green" title="E44">B1</font></span></a></span>;<br/>
<a NAME="E4:103_1"/><span class="kw">then </span>
<font color="Maroon" title="c8">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c9">j</font>) <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> 
 
<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="kw">hence </span><a NAME="E5:103_1"/>
<font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">j</font>
 <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>; <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>
<a NAME="E5:103"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c5">l</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="abcmiz_1.html#K2" title="ABCMIZ_1:func.2">Vars</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="103_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c6">z</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="c6">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c5">l</font> or <font color="Maroon" title="c6">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="abcmiz_1.html#K2" title="ABCMIZ_1:func.2">Vars</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:103_2"/>
<font color="Maroon" title="c6">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c5">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="c6">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="abcmiz_1.html#K2" title="ABCMIZ_1:func.2">Vars</a> </span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E3:103_2"/><span class="lab"><font color="Green" title="E44">C1</font></span>: 
( <font color="Maroon" title="c7">a</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="c5">l</font> &amp; <font color="Maroon" title="c6">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">l</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">a</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="c8">a</font> = <font color="Maroon" title="c7">a</font> as   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:103_2"><span class="lab"><font color="Green" title="E44">C1</font></span></a></span>;<br/>
<a NAME="E5:103_2"/>
<font color="Maroon" title="c6">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c8">a</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:103"><span class="lab"><font color="Green" title="E42">F1</font></span></a>, <a class="txt" href="#E3:103_2"><span class="lab"><font color="Green" title="E44">C1</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:103_2"/>
<font color="Maroon" title="c6">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="abcmiz_1.html#K2" title="ABCMIZ_1:func.2">Vars</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="abcmiz_1.html#T25" title="ABCMIZ_1:th.25">ABCMIZ_1:25</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">then </span><span class="kw">reconsider </span><font color="Maroon" title="c6">l</font> = <font color="Maroon" title="c5">l</font> as   <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="abcmiz_1.html#K2" title="ABCMIZ_1:func.2">Vars</a>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:103"><span class="lab"><font color="Green" title="E43">F2</font></span></a>, <a class="ref" href="finseq_1.html#D4" title="FINSEQ_1:def.4">FINSEQ_1:def 4</a></span>;<br/>
<a NAME="E7:103"/>
for <font color="Olive" title="b1">i</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><br/> for <font color="Olive" title="b2">x</font> being  <a href="abcmiz_1.html#NM3" title="ABCMIZ_1:NM.3">variable</a>  st <font color="Olive" title="b1">i</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="c6">l</font> &amp; <font color="Olive" title="b2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">l</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> holds <br/>for <font color="Olive" title="b3">y</font> being  <a href="abcmiz_1.html#NM3" title="ABCMIZ_1:NM.3">variable</a>  st <font color="Olive" title="b3">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="abcmiz_1.html#K3" title="ABCMIZ_1:func.3">vars</a> <font color="Olive" title="b2">x</font> holds <br/> ex <font color="Olive" title="b4">j</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> st <br/>( <font color="Olive" title="b4">j</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="c6">l</font> &amp; <font color="Olive" title="b4">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b1">i</font> &amp; <font color="Olive" title="b3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">l</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">j</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="103_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c7">i</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</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">x</font> being  <a href="abcmiz_1.html#NM3" title="ABCMIZ_1:NM.3">variable</a>  st <font color="Maroon" title="c7">i</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="c6">l</font> &amp; <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">l</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font> holds <br/>for <font color="Olive" title="b2">y</font> being  <a href="abcmiz_1.html#NM3" title="ABCMIZ_1:NM.3">variable</a>  st <font color="Olive" title="b2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="abcmiz_1.html#K3" title="ABCMIZ_1:func.3">vars</a> <font color="Olive" title="b1">x</font> holds <br/> ex <font color="Olive" title="b3">j</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> st <br/>( <font color="Olive" title="b3">j</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="c6">l</font> &amp; <font color="Olive" title="b3">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c7">i</font> &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">l</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">j</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c8">x</font> be   <a href="abcmiz_1.html#NM3" title="ABCMIZ_1:NM.3">variable</a>; <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="c7">i</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="c6">l</font> &amp; <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">l</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font> implies for <font color="Olive" title="b1">y</font> being  <a href="abcmiz_1.html#NM3" title="ABCMIZ_1:NM.3">variable</a>  st <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="abcmiz_1.html#K3" title="ABCMIZ_1:func.3">vars</a> <font color="Maroon" title="c8">x</font> holds <br/> ex <font color="Olive" title="b2">j</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> st <br/>( <font color="Olive" title="b2">j</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="c6">l</font> &amp; <font color="Olive" title="b2">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c7">i</font> &amp; <font color="Olive" title="b1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">l</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">j</font> ) )</span><br/>



<span class="kw">assume </span><a NAME="E1:103_3"/>
( <font color="Maroon" title="c7">i</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="c6">l</font> &amp; <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">l</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</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">y</font> being  <a href="abcmiz_1.html#NM3" title="ABCMIZ_1:NM.3">variable</a>  st <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="abcmiz_1.html#K3" title="ABCMIZ_1:func.3">vars</a> <font color="Maroon" title="c8">x</font> holds <br/> ex <font color="Olive" title="b2">j</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> st <br/>( <font color="Olive" title="b2">j</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="c6">l</font> &amp; <font color="Olive" title="b2">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c7">i</font> &amp; <font color="Olive" title="b1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">l</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">j</font> )</span><br/>

<a NAME="E2:103_3"/><span class="kw">then </span>
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c7">i</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:103"><span class="lab"><font color="Green" title="E42">F1</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:103_3"/>
for <font color="Olive" title="b1">y</font> being  <a href="abcmiz_1.html#NM3" title="ABCMIZ_1:NM.3">variable</a>  st <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="abcmiz_1.html#K3" title="ABCMIZ_1:func.3">vars</a> <font color="Maroon" title="c8">x</font> holds <br/> ex <font color="Olive" title="b2">j</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> st <br/>( <font color="Olive" title="b2">j</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="c6">l</font> &amp; <font color="Olive" title="b2">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c7">i</font> &amp; <font color="Olive" title="b1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">l</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">j</font> )
 <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>; <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">then </span><span class="kw">reconsider </span><font color="Maroon" title="c7">l</font> = <font color="Maroon" title="c6">l</font> as   <a href="abcmiz_1.html#NM4" title="ABCMIZ_1:NM.4">quasi-loci</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="abcmiz_1.html#T30" title="ABCMIZ_1:th.30">ABCMIZ_1:30</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">m</font> = <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">s</font>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c7">l</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>;<br/>
<a NAME="E9:103"/><span class="lab"><font color="Green" title="E44">A0</font></span>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="abcmiz_1.html#K27" title="ABCMIZ_1:func.27">MaxConstrSign</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><a href="abcmiz_1.html#K6" title="ABCMIZ_1:func.6">a_Type</a> ,<a href="abcmiz_1.html#K7" title="ABCMIZ_1:func.7">an_Adj</a> ,<a href="abcmiz_1.html#K8" title="ABCMIZ_1:func.8">a_Term</a> </span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="abcmiz_1.html#D9" title="ABCMIZ_1:def.9">ABCMIZ_1:def 9</a></span>;<br/>
<a NAME="E10:103"/><span class="lab"><font color="Green" title="E45">A1</font></span>: 
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">s</font>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c7">l</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="abcmiz_1.html#K20" title="ABCMIZ_1:func.20">Constructors</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:103"><span class="lab"><font color="Green" title="E44">A0</font></span></a>, <a class="ref" href="abcmiz_a.html#T28" target="_self" title="ABCMIZ_A:th.28">ThCs</a></span>;<br/>
<a NAME="E11:103"/><span class="kw">then </span>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">s</font>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c7">l</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="abcmiz_1.html#K9" title="ABCMIZ_1:func.9">*</a> ,<a href="abcmiz_1.html#K10" title="ABCMIZ_1:func.10">non_op</a> </span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="abcmiz_1.html#K20" title="ABCMIZ_1:func.20">Constructors</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c9">m</font> = <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">s</font>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c7">l</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> as   <a href="abcmiz_1.html#V2" title="ABCMIZ_1:attr.2">constructor</a>  <a href="msualg_1.html#NM2" title="MSUALG_1:NM.2">OperSymbol</a> of <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="#E10:103"><span class="lab"><font color="Green" title="E45">A1</font></span></a>, <a class="ref" href="abcmiz_a.html#T42" target="_self" title="ABCMIZ_A:th.42">ThCc</a>, <a class="ref" href="abcmiz_1.html#D24" title="ABCMIZ_1:def.24">ABCMIZ_1:def 24</a></span>;<br/>
 <a href="msualg_1.html#K2" title="MSUALG_1:func.2">the_result_sort_of</a> <font color="Maroon" title="c9">m</font> = 
<font color="Maroon" title="c9">m</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="abcmiz_1.html#D24" title="ABCMIZ_1:def.24">ABCMIZ_1:def 24</a></span>
<br/>.= 
<font color="Maroon" title="c4">s</font>
<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="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c10">m</font> = <font color="Maroon" title="c9">m</font> as   <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="c4">s</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="abcmiz_1.html#D32" title="ABCMIZ_1:def.32">ABCMIZ_1:def 32</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c10">m</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="c10">m</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">n</font></span><br/>

<span class="kw">thus </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="c10">m</font></span>)</span> = 
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">m</font> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> </span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="abcmiz_1.html#D24" title="ABCMIZ_1:def.24">ABCMIZ_1:def 24</a></span>
<br/>.= 
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c7">l</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="abcmiz_1.html#K21" title="ABCMIZ_1:func.21">`1</a> </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/>.= 
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c7">l</font>
<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/>.= 
<font color="Maroon" title="c3">n</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:103"><span class="lab"><font color="Green" title="E41">F0</font></span></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>
