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<b>reconsider </b><font color="Maroon">c<sub>2</sub></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">c<sub>1</sub></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">c<sub>1</sub></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><a class="ref" href="msualg_1.html#T7" target="_self">Th7</a></i>;<br/>
<a NAME="E2:24_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">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></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">c<sub>1</sub></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">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></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">c<sub>1</sub></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">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></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">c<sub>1</sub></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">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></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">c<sub>1</sub></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> )
 
<b>by </b><i><a class="txt" href="msualg_1.html#E24"><i><font color="Green">Lemma9</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:24_1_1"/>
( ex <font color="Olive">b<sub>1</sub></font> being <a href="realset2.html#V3">trivial</a> <a href="msualg_1.html#V1" target="_self">strict</a> non <a href="msualg_1.html#V2" target="_self">void</a> <a href="msualg_1.html#V6" target="_self">segmental</a>  <a href="msualg_1.html#L1" target="_self">ManySortedSign</a>  st <br/>( the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span> &amp; the <a href="msualg_1.html#U1" target="_self">OperSymbols</a> of <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <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">c<sub>1</sub></font></span>)</span> &amp; the <a href="msualg_1.html#U2" target="_self">Arity</a> of <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <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">c<sub>1</sub></font></span>)</span> &amp; the <a href="msualg_1.html#U3" target="_self">ResultSort</a> of <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <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">c<sub>1</sub></font></span>)</span></span>)</span> <a href="pboole.html#K9">--&gt;</a> 0 ) &amp; ( for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being <a href="realset2.html#V3">trivial</a> <a href="msualg_1.html#V1" target="_self">strict</a> non <a href="msualg_1.html#V2" target="_self">void</a> <a href="msualg_1.html#V6" target="_self">segmental</a>  <a href="msualg_1.html#L1" target="_self">ManySortedSign</a>  st the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span> &amp; the <a href="msualg_1.html#U1" target="_self">OperSymbols</a> of <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <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">c<sub>1</sub></font></span>)</span> &amp; the <a href="msualg_1.html#U2" target="_self">Arity</a> of <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <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">c<sub>1</sub></font></span>)</span> &amp; the <a href="msualg_1.html#U3" target="_self">ResultSort</a> of <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <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">c<sub>1</sub></font></span>)</span></span>)</span> <a href="pboole.html#K9">--&gt;</a> 0 &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span> &amp; the <a href="msualg_1.html#U1" target="_self">OperSymbols</a> of <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <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">c<sub>1</sub></font></span>)</span> &amp; the <a href="msualg_1.html#U2" target="_self">Arity</a> of <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <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">c<sub>1</sub></font></span>)</span> &amp; the <a href="msualg_1.html#U3" target="_self">ResultSort</a> of <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <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">c<sub>1</sub></font></span>)</span></span>)</span> <a href="pboole.html#K9">--&gt;</a> 0 holds <br/><font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> ) )
 ;<br/>


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