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<b>consider </b><font color="Maroon">A</font> being   <a href="unialg_1.html#NM2">Universal_Algebra</a>;<br/>
<b>reconsider </b><font color="Maroon">f</font> = <span class="p1">(<span class="default"><a href="pboole.html#K8">*--&gt;</a> 0</span>)</span> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K6" target="_self">signature</a> <font color="Maroon">A</font></span>)</span> as   <a href="funct_2.html#NM1">Function</a> of  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K6" target="_self">signature</a> <font color="Maroon">A</font></span>)</span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span> <a href="finseq_2.html#K3">*</a>  <b>by </b><i/>;<br/>
<a NAME="E3:23_1_1"/>
(  <a href="msualg_1.html#G1" target="_self">ManySortedSign</a>(# <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K6" target="_self">signature</a> <font color="Maroon">A</font></span>)</span></span>)</span>,<font color="Maroon">f</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p3">(<span class="default"><a href="msualg_1.html#K6" target="_self">signature</a> <font color="Maroon">A</font></span>)</span></span>)</span> <a href="pboole.html#K9">--&gt;</a> 0</span>)</span> #) is <a href="msualg_1.html#V6" target="_self">segmental</a> &amp;  <a href="msualg_1.html#G1" target="_self">ManySortedSign</a>(# <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K6" target="_self">signature</a> <font color="Maroon">A</font></span>)</span></span>)</span>,<font color="Maroon">f</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p3">(<span class="default"><a href="msualg_1.html#K6" target="_self">signature</a> <font color="Maroon">A</font></span>)</span></span>)</span> <a href="pboole.html#K9">--&gt;</a> 0</span>)</span> #) is <a href="realset2.html#V3">trivial</a> &amp; not  <a href="msualg_1.html#G1" target="_self">ManySortedSign</a>(# <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K6" target="_self">signature</a> <font color="Maroon">A</font></span>)</span></span>)</span>,<font color="Maroon">f</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p3">(<span class="default"><a href="msualg_1.html#K6" target="_self">signature</a> <font color="Maroon">A</font></span>)</span></span>)</span> <a href="pboole.html#K9">--&gt;</a> 0</span>)</span> #) is <a href="msualg_1.html#V2" target="_self">void</a> &amp;  <a href="msualg_1.html#G1" target="_self">ManySortedSign</a>(# <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K6" target="_self">signature</a> <font color="Maroon">A</font></span>)</span></span>)</span>,<font color="Maroon">f</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p3">(<span class="default"><a href="msualg_1.html#K6" target="_self">signature</a> <font color="Maroon">A</font></span>)</span></span>)</span> <a href="pboole.html#K9">--&gt;</a> 0</span>)</span> #) is <a href="msualg_1.html#V1" target="_self">strict</a> &amp; not  <a href="msualg_1.html#G1" target="_self">ManySortedSign</a>(# <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K6" target="_self">signature</a> <font color="Maroon">A</font></span>)</span></span>)</span>,<font color="Maroon">f</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p3">(<span class="default"><a href="msualg_1.html#K6" target="_self">signature</a> <font color="Maroon">A</font></span>)</span></span>)</span> <a href="pboole.html#K9">--&gt;</a> 0</span>)</span> #) is <a href="struct_0.html#V3">empty</a> )
 
<b>by </b><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" target="_self">ManySortedSign</a>  st <br/>( <font color="Olive">b<sub>1</sub></font> is <a href="msualg_1.html#V6" target="_self">segmental</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="realset2.html#V3">trivial</a> &amp; not <font color="Olive">b<sub>1</sub></font> is <a href="msualg_1.html#V2" target="_self">void</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="msualg_1.html#V1" target="_self">strict</a> &amp; not <font color="Olive">b<sub>1</sub></font> is <a href="struct_0.html#V3">empty</a> )
 ;<br/>


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