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<b>thus </b><a NAME="E1:67_1_1"/>
not the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="pua2mss1.html#K11" target="_self">MSSign</a> <font color="Maroon">A</font>,<font color="Maroon">P</font></span>)</span> is <a href="xboole_0.html#V1">empty</a>
 <b>by </b><i><a class="ref" href="pua2mss1.html#T1" target="_self">Th1</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="struct_0.html#D1">STRUCT_0:def 1</a><br/>

<b>consider </b><font color="Maroon">g</font> being   <a href="pua2mss1.html#NM2">OperSymbol</a> of <font color="Maroon">A</font>;<br/>
<b>consider </b><font color="Maroon">x</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="pua2mss1.html#K2" target="_self">Den</a> <font color="Maroon">g</font>,<font color="Maroon">A</font></span>)</span>;<br/>
<b>reconsider </b><font color="Maroon">x</font> = <font color="Maroon">x</font> as    <a href="finseq_2.html#M2">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font> <a href="finseq_2.html#K3">*</a>  ;<br/>
<a NAME="E5:67_1_1"/>
(  <a href="setfam_1.html#K5">union</a> <font color="Maroon">P</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font> &amp;  <a href="relset_1.html#K5">rng</a> <font color="Maroon">x</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font> )
 
<b>by </b><i><a class="ref" href="eqrel_1.html#D6">EQREL_1:def 6</a></i>;<br/>
<b>then consider </b><font color="Maroon">q</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E7:67_1_1"/><i><font color="Green">E29</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">q</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">x</font> &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">q</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">P</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="card_3.html#K4">product</a> <font color="Maroon">q</font> )
 <b>by </b><i/>;<br/>
<a NAME="E8:67_1_1"/>
 <a href="finseq_1.html#K4">dom</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">x</font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">q</font> = <font color="Maroon">q</font> as   <a href="finseq_1.html#NM1">FinSequence</a> <b>by </b><i>, <a class="ref" href="finseq_1.html#D2">FINSEQ_1:def 2</a></i>;<br/>
<b>reconsider </b><font color="Maroon">q</font> = <font color="Maroon">q</font> as    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">P</font> <b>by </b><i>, <a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/>
<b>reconsider </b><font color="Maroon">q</font> = <font color="Maroon">q</font> as    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">P</font> <a href="finseq_2.html#K3">*</a>  <b>by </b><i><a class="ref" href="finseq_1.html#D11">FINSEQ_1:def 11</a></i>;<br/>
<a NAME="E12:67_1_1"/>
(  <a href="card_3.html#K4">product</a> <font color="Maroon">q</font> <a href="subset_1.html#R2">meets</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="pua2mss1.html#K2" target="_self">Den</a> <font color="Maroon">g</font>,<font color="Maroon">A</font></span>)</span> &amp; the <a href="msualg_1.html#U1">OperSymbols</a> of <span class="p1">(<span class="default"><a href="pua2mss1.html#K11" target="_self">MSSign</a> <font color="Maroon">A</font>,<font color="Maroon">P</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">f</font>,<font color="Olive">p</font></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">f</font> is   <a href="pua2mss1.html#NM2">OperSymbol</a> of <font color="Maroon">A</font>, <font color="Olive">p</font> is    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">P</font> <a href="finseq_2.html#K3">*</a>  :  <a href="card_3.html#K4">product</a> <font color="Olive">p</font> <a href="subset_1.html#R2">meets</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="pua2mss1.html#K2" target="_self">Den</a> <font color="Olive">f</font>,<font color="Maroon">A</font></span>)</span> </span>}</span>  )
 
<b>by </b><i>, <a class="ref" href="pua2mss1.html#T1" target="_self">Th1</a>, <a class="ref" href="xboole_0.html#T3">XBOOLE_0:3</a></i>;<br/>
<a NAME="E13:67_1_1"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">g</font>,<font color="Maroon">q</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <span class="p1">(<span class="default"><a href="pua2mss1.html#K11" target="_self">MSSign</a> <font color="Maroon">A</font>,<font color="Maroon">P</font></span>)</span>
 
;<br/>
<b>hence </b><a NAME="E14:67_1_1"/>
the <a href="msualg_1.html#U1">OperSymbols</a> of <span class="p1">(<span class="default"><a href="pua2mss1.html#K11" target="_self">MSSign</a> <font color="Maroon">A</font>,<font color="Maroon">P</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="msualg_1.html#D5">MSUALG_1:def 5</a><br/>


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