<?xml version="1.0"?>
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<b>let </b><font color="Maroon" title="c1">C1</font>, <font color="Maroon" title="c2">C2</font> be  <a href="msualg_1.html#V1" title="MSUALG_1:attr.1">strict</a> <a href="catalg_1.html#NM1" title="CATALG_1:NM.1">Signature</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">C1</font> is <a href="abcmiz_1.html#V1" title="ABCMIZ_1:attr.1">constructor</a> &amp; the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <font color="Maroon" title="c1">C1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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> &amp; <font color="Maroon" title="c2">C2</font> is <a href="abcmiz_1.html#V1" title="ABCMIZ_1:attr.1">constructor</a> &amp; the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <font color="Maroon" title="c2">C2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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> implies <font color="Maroon" title="c1">C1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">C2</font> )</span><br/>

<b>assume </b><b>that </b><br/><a NAME="E1:58_1_2"/><i><font color="Green" title="E36">A1</font></i>: 
( <font color="Maroon" title="c1">C1</font> is <a href="abcmiz_1.html#V1" title="ABCMIZ_1:attr.1">constructor</a> &amp; the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <font color="Maroon" title="c1">C1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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> )
 <b>and </b><br/><a NAME="E2:58_1_2"/><i><font color="Green" title="E37">A2</font></i>: 
( <font color="Maroon" title="c2">C2</font> is <a href="abcmiz_1.html#V1" title="ABCMIZ_1:attr.1">constructor</a> &amp; the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <font color="Maroon" title="c2">C2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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 class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">C1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">C2</font></span><br/>

<b>set </b><font color="Maroon" title="c3">A</font> = <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>;<br/>
<a NAME="E3:58_1_2"/><i><font color="Green" title="E38">A3</font></i>: 
( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C1</font> <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> &amp; the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">C2</font> <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> )
 
<b>by </b><i><a class="txt" href="abcmiz_1.html#E1:58_1_2"><i><font color="Green" title="E36">A1</font></i></a>, <a class="txt" href="abcmiz_1.html#E2:58_1_2"><i><font color="Green" title="E37">A2</font></i></a>, <a class="ref" href="abcmiz_1.html#D9" target="_self" title="ABCMIZ_1:def.9">CONSTRSIGN</a></i>;<br/>
<a NAME="E4:58_1_2"/><i><font color="Green" title="E39">A4</font></i>: 
( the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">Arity</a> of <font color="Maroon" title="c1">C1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="abcmiz_1.html#K9" title="ABCMIZ_1:func.9">*</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><a href="abcmiz_1.html#K7" title="ABCMIZ_1:func.7">an_Adj</a> ,<a href="abcmiz_1.html#K6" title="ABCMIZ_1:func.6">a_Type</a> </span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> &amp; the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">Arity</a> of <font color="Maroon" title="c2">C2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="abcmiz_1.html#K9" title="ABCMIZ_1:func.9">*</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><a href="abcmiz_1.html#K7" title="ABCMIZ_1:func.7">an_Adj</a> ,<a href="abcmiz_1.html#K6" title="ABCMIZ_1:func.6">a_Type</a> </span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> )
 
<b>by </b><i><a class="txt" href="abcmiz_1.html#E1:58_1_2"><i><font color="Green" title="E36">A1</font></i></a>, <a class="txt" href="abcmiz_1.html#E2:58_1_2"><i><font color="Green" title="E37">A2</font></i></a>, <a class="ref" href="abcmiz_1.html#D9" target="_self" title="ABCMIZ_1:def.9">CONSTRSIGN</a></i>;<br/>
<a NAME="E5:58_1_2"/><i><font color="Green" title="E40">A5</font></i>: 
( the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">Arity</a> of <font color="Maroon" title="c1">C1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="abcmiz_1.html#K10" title="ABCMIZ_1:func.10">non_op</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><a href="abcmiz_1.html#K7" title="ABCMIZ_1:func.7">an_Adj</a> </span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span> &amp; the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">Arity</a> of <font color="Maroon" title="c2">C2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="abcmiz_1.html#K10" title="ABCMIZ_1:func.10">non_op</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><a href="abcmiz_1.html#K7" title="ABCMIZ_1:func.7">an_Adj</a> </span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span> )
 
<b>by </b><i><a class="txt" href="abcmiz_1.html#E1:58_1_2"><i><font color="Green" title="E36">A1</font></i></a>, <a class="txt" href="abcmiz_1.html#E2:58_1_2"><i><font color="Green" title="E37">A2</font></i></a>, <a class="ref" href="abcmiz_1.html#D9" target="_self" title="ABCMIZ_1:def.9">CONSTRSIGN</a></i>;<br/>
<a NAME="E6:58_1_2"/><i><font color="Green" title="E41">A6</font></i>: 
( the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">ResultSort</a> of <font color="Maroon" title="c1">C1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="abcmiz_1.html#K9" title="ABCMIZ_1:func.9">*</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="abcmiz_1.html#K6" title="ABCMIZ_1:func.6">a_Type</a>  &amp; the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">ResultSort</a> of <font color="Maroon" title="c2">C2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="abcmiz_1.html#K9" title="ABCMIZ_1:func.9">*</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="abcmiz_1.html#K6" title="ABCMIZ_1:func.6">a_Type</a>  )
 
<b>by </b><i><a class="txt" href="abcmiz_1.html#E1:58_1_2"><i><font color="Green" title="E36">A1</font></i></a>, <a class="txt" href="abcmiz_1.html#E2:58_1_2"><i><font color="Green" title="E37">A2</font></i></a>, <a class="ref" href="abcmiz_1.html#D9" target="_self" title="ABCMIZ_1:def.9">CONSTRSIGN</a></i>;<br/>
<a NAME="E7:58_1_2"/><i><font color="Green" title="E42">A7</font></i>: 
( the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">ResultSort</a> of <font color="Maroon" title="c1">C1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="abcmiz_1.html#K10" title="ABCMIZ_1:func.10">non_op</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="abcmiz_1.html#K7" title="ABCMIZ_1:func.7">an_Adj</a>  &amp; the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">ResultSort</a> of <font color="Maroon" title="c2">C2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="abcmiz_1.html#K10" title="ABCMIZ_1:func.10">non_op</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="abcmiz_1.html#K7" title="ABCMIZ_1:func.7">an_Adj</a>  )
 
<b>by </b><i><a class="txt" href="abcmiz_1.html#E1:58_1_2"><i><font color="Green" title="E36">A1</font></i></a>, <a class="txt" href="abcmiz_1.html#E2:58_1_2"><i><font color="Green" title="E37">A2</font></i></a>, <a class="ref" href="abcmiz_1.html#D9" target="_self" title="ABCMIZ_1:def.9">CONSTRSIGN</a></i>;<br/>
<a NAME="E8:58_1_2"/>
(  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">Arity</a> of <font color="Maroon" title="c1">C1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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> &amp;  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">Arity</a> of <font color="Maroon" title="c2">C2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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> )
 
<b>by </b><i><a class="txt" href="abcmiz_1.html#E1:58_1_2"><i><font color="Green" title="E36">A1</font></i></a>, <a class="txt" href="abcmiz_1.html#E2:58_1_2"><i><font color="Green" title="E37">A2</font></i></a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E9:58_1_2"/><b>then </b><i><font color="Green" title="E43">A8</font></i>: 
( the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">Arity</a> of <font color="Maroon" title="c1">C1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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>  <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><a href="abcmiz_1.html#K7" title="ABCMIZ_1:func.7">an_Adj</a> ,<a href="abcmiz_1.html#K6" title="ABCMIZ_1:func.6">a_Type</a> </span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<span class="p1"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><a href="abcmiz_1.html#K7" title="ABCMIZ_1:func.7">an_Adj</a> </span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span> &amp; the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">Arity</a> of <font color="Maroon" title="c2">C2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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>  <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><a href="abcmiz_1.html#K7" title="ABCMIZ_1:func.7">an_Adj</a> ,<a href="abcmiz_1.html#K6" title="ABCMIZ_1:func.6">a_Type</a> </span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>,<span class="p1"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><a href="abcmiz_1.html#K7" title="ABCMIZ_1:func.7">an_Adj</a> </span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span> )
 
<b>by </b><i><a class="txt" href="abcmiz_1.html#E4:58_1_2"><i><font color="Green" title="E39">A4</font></i></a>, <a class="txt" href="abcmiz_1.html#E5:58_1_2"><i><font color="Green" title="E40">A5</font></i></a>, <a class="ref" href="funct_4.html#T69" title="FUNCT_4:th.69">FUNCT_4:69</a></i>;<br/>
<a NAME="E10:58_1_2"/>
(  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">ResultSort</a> of <font color="Maroon" title="c1">C1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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> &amp;  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">ResultSort</a> of <font color="Maroon" title="c2">C2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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> )
 
<b>by </b><i><a class="txt" href="abcmiz_1.html#E1:58_1_2"><i><font color="Green" title="E36">A1</font></i></a>, <a class="txt" href="abcmiz_1.html#E2:58_1_2"><i><font color="Green" title="E37">A2</font></i></a>, <a class="txt" href="abcmiz_1.html#E3:58_1_2"><i><font color="Green" title="E38">A3</font></i></a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E11:58_1_2"/><b>then </b>
( the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">ResultSort</a> of <font color="Maroon" title="c1">C1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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>  <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <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>  &amp; the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">ResultSort</a> of <font color="Maroon" title="c2">C2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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>  <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <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>  )
 
<b>by </b><i><a class="txt" href="abcmiz_1.html#E6:58_1_2"><i><font color="Green" title="E41">A6</font></i></a>, <a class="txt" href="abcmiz_1.html#E7:58_1_2"><i><font color="Green" title="E42">A7</font></i></a>, <a class="ref" href="funct_4.html#T69" title="FUNCT_4:th.69">FUNCT_4:69</a></i>;<br/>
<b>hence </b><a NAME="E12:58_1_2"/>
<font color="Maroon" title="c1">C1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">C2</font>
 <b>by </b><i><a class="txt" href="abcmiz_1.html#E1:58_1_2"><i><font color="Green" title="E36">A1</font></i></a>, <a class="txt" href="abcmiz_1.html#E2:58_1_2"><i><font color="Green" title="E37">A2</font></i></a>, <a class="txt" href="abcmiz_1.html#E3:58_1_2"><i><font color="Green" title="E38">A3</font></i></a>, <a class="txt" href="abcmiz_1.html#E9:58_1_2"><i><font color="Green" title="E43">A8</font></i></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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