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<b>consider </b><font color="Maroon" title="c1">A</font> being   <a href="unialg_1.html#NM2" title="UNIALG_1:NM.2">Universal_Algebra</a>;<br/>
<b>reconsider </b><font color="Maroon" title="c2">f</font> = <span class="p1">(<span class="default"><a href="pboole.html#K8" title="PBOOLE:func.8">*--&gt;</a> 0</span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c1">A</font></span>)</span> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c1">A</font></span>)</span>,<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default">0</span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  <b>by </b><i><a class="ref" href="msualg_1.html#T7" target="_self" title="MSUALG_1:th.7">Th7</a></i>;<br/>
<a NAME="E3:23_1_1"/>
(  <a href="msualg_1.html#G1" title="MSUALG_1:aggr.1">ManySortedSign</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default">0</span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c1">A</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">f</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p3">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c1">A</font></span>)</span></span>)</span> <a href="pboole.html#K9" title="PBOOLE:func.9">--&gt;</a> 0</span>)</span> #) is <a href="msualg_1.html#V6" title="MSUALG_1:attr.6">segmental</a> &amp;  <a href="msualg_1.html#G1" title="MSUALG_1:aggr.1">ManySortedSign</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default">0</span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c1">A</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">f</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p3">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c1">A</font></span>)</span></span>)</span> <a href="pboole.html#K9" title="PBOOLE:func.9">--&gt;</a> 0</span>)</span> #) is <a href="realset2.html#V3" title="REALSET2:attr.3">trivial</a> &amp; not  <a href="msualg_1.html#G1" title="MSUALG_1:aggr.1">ManySortedSign</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default">0</span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c1">A</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">f</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p3">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c1">A</font></span>)</span></span>)</span> <a href="pboole.html#K9" title="PBOOLE:func.9">--&gt;</a> 0</span>)</span> #) is <a href="msualg_1.html#V2" title="MSUALG_1:attr.2">void</a> &amp;  <a href="msualg_1.html#G1" title="MSUALG_1:aggr.1">ManySortedSign</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default">0</span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c1">A</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">f</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p3">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c1">A</font></span>)</span></span>)</span> <a href="pboole.html#K9" title="PBOOLE:func.9">--&gt;</a> 0</span>)</span> #) is <a href="msualg_1.html#V1" title="MSUALG_1:attr.1">strict</a> &amp; not  <a href="msualg_1.html#G1" title="MSUALG_1:aggr.1">ManySortedSign</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default">0</span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c1">A</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">f</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p3">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">signature</a> <font color="Maroon" title="c1">A</font></span>)</span></span>)</span> <a href="pboole.html#K9" title="PBOOLE:func.9">--&gt;</a> 0</span>)</span> #) is <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> )
 
<b>by </b><i><a class="txt" href="msualg_1.html#E24"><i><font color="Green" title="E9">Lm2</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:23_1_1"/>
 ex <font color="Olive">b<sub>1</sub></font> being   <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a>  st <br/>( <font color="Olive">b<sub>1</sub></font> is <a href="msualg_1.html#V6" title="MSUALG_1:attr.6">segmental</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="realset2.html#V3" title="REALSET2:attr.3">trivial</a> &amp; not <font color="Olive">b<sub>1</sub></font> is <a href="msualg_1.html#V2" title="MSUALG_1:attr.2">void</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="msualg_1.html#V1" title="MSUALG_1:attr.1">strict</a> &amp; not <font color="Olive">b<sub>1</sub></font> is <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> )
 ;<br/>


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