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<b>let </b><font color="Maroon" title="c1">C</font> be   <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">C</font> is <a href="abcmiz_1.html#V1" title="ABCMIZ_1:attr.1">constructor</a> implies ( not <font color="Maroon" title="c1">C</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> &amp; not <font color="Maroon" title="c1">C</font> is <a href="msualg_1.html#V2" title="MSUALG_1:attr.2">void</a> ) )</span><br/>

<b>assume </b><a NAME="E1:57_1_1"/><i><font color="Green" title="E36">A1</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</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>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="abcmiz_1.html#D9" target="_self" title="ABCMIZ_1:def.9">ABCMIZ_1:def 9</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <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="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <font color="Maroon" title="c1">C</font> or  not the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">Arity</a> of <font color="Maroon" title="c1">C</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> or  not the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">Arity</a> of <font color="Maroon" title="c1">C</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> or  not the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">ResultSort</a> of <font color="Maroon" title="c1">C</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>  or  not the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">ResultSort</a> of <font color="Maroon" title="c1">C</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>  or  ex <font color="Olive" title="b1">o</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <font color="Maroon" title="c1">C</font> st <br/>( <font color="Olive" title="b1">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="abcmiz_1.html#K9" title="ABCMIZ_1:func.9">*</a>  &amp; <font color="Olive" title="b1">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="abcmiz_1.html#K10" title="ABCMIZ_1:func.10">non_op</a>  &amp; not the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">Arity</a> of <font color="Maroon" title="c1">C</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">o</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"><a href="abcmiz_1.html#K8" title="ABCMIZ_1:func.8">a_Term</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  ) or ( not <font color="Maroon" title="c1">C</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> &amp; not <font color="Maroon" title="c1">C</font> is <a href="msualg_1.html#V2" title="MSUALG_1:attr.2">void</a> ) )</span><br/>

<b>assume </b><a NAME="E2:57_1_1"/>
<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="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <font color="Maroon" title="c1">C</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">Arity</a> of <font color="Maroon" title="c1">C</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> or  not the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">Arity</a> of <font color="Maroon" title="c1">C</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> or  not the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">ResultSort</a> of <font color="Maroon" title="c1">C</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>  or  not the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">ResultSort</a> of <font color="Maroon" title="c1">C</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>  or  ex <font color="Olive" title="b1">o</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <font color="Maroon" title="c1">C</font> st <br/>( <font color="Olive" title="b1">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="abcmiz_1.html#K9" title="ABCMIZ_1:func.9">*</a>  &amp; <font color="Olive" title="b1">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="abcmiz_1.html#K10" title="ABCMIZ_1:func.10">non_op</a>  &amp; not the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">Arity</a> of <font color="Maroon" title="c1">C</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">o</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"><a href="abcmiz_1.html#K8" title="ABCMIZ_1:func.8">a_Term</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  ) or ( not <font color="Maroon" title="c1">C</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> &amp; not <font color="Maroon" title="c1">C</font> is <a href="msualg_1.html#V2" title="MSUALG_1:attr.2">void</a> ) )</span><br/>

<a NAME="E3:57_1_1"/><b>then </b>
the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <font color="Maroon" title="c1">C</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<b>by </b><i><a class="ref" href="xboole_1.html#T3" title="XBOOLE_1:th.3">XBOOLE_1:3</a></i>;<br/>
<b>hence </b><a NAME="E4:57_1_1"/>
(  not the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">Arity</a> of <font color="Maroon" title="c1">C</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> or  not the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">Arity</a> of <font color="Maroon" title="c1">C</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> or  not the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">ResultSort</a> of <font color="Maroon" title="c1">C</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>  or  not the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">ResultSort</a> of <font color="Maroon" title="c1">C</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>  or  ex <font color="Olive" title="b1">o</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <font color="Maroon" title="c1">C</font> st <br/>( <font color="Olive" title="b1">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="abcmiz_1.html#K9" title="ABCMIZ_1:func.9">*</a>  &amp; <font color="Olive" title="b1">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="abcmiz_1.html#K10" title="ABCMIZ_1:func.10">non_op</a>  &amp; not the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">Arity</a> of <font color="Maroon" title="c1">C</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">o</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"><a href="abcmiz_1.html#K8" title="ABCMIZ_1:func.8">a_Term</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  ) or ( not <font color="Maroon" title="c1">C</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> &amp; not <font color="Maroon" title="c1">C</font> is <a href="msualg_1.html#V2" title="MSUALG_1:attr.2">void</a> ) )
 <b>by </b><i><a class="txt" href="abcmiz_1.html#E1:57_1_1"><i><font color="Green" title="E36">A1</font></i></a>, <a class="ref" href="struct_0.html#D1" title="STRUCT_0:def.1">STRUCT_0:def 1</a>, <a class="ref" href="msualg_1.html#D5" title="MSUALG_1:def.5">MSUALG_1:def 5</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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