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<a NAME="E1:14_1_1"/><i><font color="Green">E24</font></i>: 
(  <a href="relat_1.html#K1">dom</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S1</font> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S1</font> &amp;  <a href="relat_1.html#K1">dom</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S2</font> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S2</font> )
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E2:14_1_1"/><i><font color="Green">E33</font></i>: 
(  <a href="relat_1.html#K1">dom</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S1</font> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S1</font> &amp;  <a href="relat_1.html#K1">dom</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S2</font> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S2</font> )
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<b>reconsider </b><font color="Maroon">CARR</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S1</font> <a href="xboole_0.html#K2">\/</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S2</font> as  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a>  ;<br/>
<b>set </b><font color="Maroon">OPER</font> = the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S1</font> <a href="xboole_0.html#K2">\/</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S2</font>;<br/>
<b>set </b><font color="Maroon">ARITY</font> = the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S1</font> <a href="funct_4.html#K1">+*</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S2</font>;<br/>
<b>set </b><font color="Maroon">RESULT</font> = the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S1</font> <a href="funct_4.html#K1">+*</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S2</font>;<br/>
<a NAME="E4:14_1_1"/>
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">CARR</font> &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S2</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">CARR</font> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E5:14_1_1"/><b>then </b>
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S1</font> <a href="finseq_2.html#K3">*</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">CARR</font> <a href="finseq_2.html#K3">*</a>  &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S2</font> <a href="finseq_2.html#K3">*</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">CARR</font> <a href="finseq_2.html#K3">*</a>  &amp;  <a href="relat_1.html#K2">rng</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S1</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S1</font> <a href="finseq_2.html#K3">*</a>  &amp;  <a href="relat_1.html#K2">rng</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S2</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S2</font> <a href="finseq_2.html#K3">*</a>  )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T83">FINSEQ_1:83</a>, <a class="ref" href="relset_1.html#T12">RELSET_1:12</a></i>;<br/>
<a NAME="E6:14_1_1"/><b>then </b>
(  <a href="relat_1.html#K2">rng</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">CARR</font> <a href="finseq_2.html#K3">*</a>  &amp;  <a href="relat_1.html#K2">rng</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S2</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">CARR</font> <a href="finseq_2.html#K3">*</a>  )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E7:14_1_1"/><b>then </b>
(  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default">the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S1</font> <a href="funct_4.html#K1">+*</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S2</font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S1</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S2</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S1</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S2</font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">CARR</font> <a href="finseq_2.html#K3">*</a>  )
 
<b>by </b><i><a class="ref" href="funct_4.html#T18">FUNCT_4:18</a>, <a class="ref" href="xboole_1.html#T8">XBOOLE_1:8</a></i>;<br/>
<a NAME="E8:14_1_1"/><b>then </b>
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default">the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S1</font> <a href="funct_4.html#K1">+*</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S2</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S1</font> <a href="xboole_0.html#K2">\/</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S2</font> &amp;  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default">the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S1</font> <a href="funct_4.html#K1">+*</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S2</font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">CARR</font> <a href="finseq_2.html#K3">*</a>  )
 
<b>by </b><i>, <a class="ref" href="funct_4.html#D1">FUNCT_4:def 1</a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">ARITY</font> = the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S1</font> <a href="funct_4.html#K1">+*</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S2</font> as   <a href="funct_2.html#NM1">Function</a> of the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S1</font> <a href="xboole_0.html#K2">\/</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S2</font>,<font color="Maroon">CARR</font> <a href="finseq_2.html#K3">*</a>  <b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a>, <a class="ref" href="relset_1.html#T11">RELSET_1:11</a></i>;<br/>
<a NAME="E10:14_1_1"/>
(  <a href="relat_1.html#K2">rng</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S1</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S1</font> &amp;  <a href="relat_1.html#K2">rng</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S2</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S2</font> &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">CARR</font> &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S2</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">CARR</font> )
 
<b>by </b><i><a class="ref" href="relset_1.html#T12">RELSET_1:12</a>, <a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E11:14_1_1"/><b>then </b>
(  <a href="relat_1.html#K2">rng</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">CARR</font> &amp;  <a href="relat_1.html#K2">rng</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S2</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">CARR</font> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E12:14_1_1"/><b>then </b>
(  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default">the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S1</font> <a href="funct_4.html#K1">+*</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S2</font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S1</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S2</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S1</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S2</font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">CARR</font> )
 
<b>by </b><i><a class="ref" href="funct_4.html#T18">FUNCT_4:18</a>, <a class="ref" href="xboole_1.html#T8">XBOOLE_1:8</a></i>;<br/>
<a NAME="E13:14_1_1"/><b>then </b>
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default">the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S1</font> <a href="funct_4.html#K1">+*</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S2</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S1</font> <a href="xboole_0.html#K2">\/</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S2</font> &amp;  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default">the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S1</font> <a href="funct_4.html#K1">+*</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S2</font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">CARR</font> )
 
<b>by </b><i>, <a class="ref" href="funct_4.html#D1">FUNCT_4:def 1</a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">RESULT</font> = the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S1</font> <a href="funct_4.html#K1">+*</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S2</font> as   <a href="funct_2.html#NM1">Function</a> of the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S1</font> <a href="xboole_0.html#K2">\/</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S2</font>,<font color="Maroon">CARR</font> <b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a>, <a class="ref" href="relset_1.html#T11">RELSET_1:11</a></i>;<br/>
<b>take </b>
 <a href="msualg_1.html#G1">ManySortedSign</a>(# <font color="Maroon">CARR</font>,<span class="p1">(<span class="default">the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S1</font> <a href="xboole_0.html#K2">\/</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S2</font></span>)</span>,<font color="Maroon">ARITY</font>,<font color="Maroon">RESULT</font> #)
;<br/>

<b>thus </b><a NAME="E15:14_1_1"/>
( the <a href="struct_0.html#U1">carrier</a> of <a href="msualg_1.html#G1">ManySortedSign</a>(# <font color="Maroon">CARR</font>,<span class="p1">(<span class="default">the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S1</font> <a href="xboole_0.html#K2">\/</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S2</font></span>)</span>,<font color="Maroon">ARITY</font>,<font color="Maroon">RESULT</font> #) <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S1</font> <a href="xboole_0.html#K2">\/</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S2</font> &amp; the <a href="msualg_1.html#U1">OperSymbols</a> of <a href="msualg_1.html#G1">ManySortedSign</a>(# <font color="Maroon">CARR</font>,<span class="p1">(<span class="default">the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S1</font> <a href="xboole_0.html#K2">\/</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S2</font></span>)</span>,<font color="Maroon">ARITY</font>,<font color="Maroon">RESULT</font> #) <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S1</font> <a href="xboole_0.html#K2">\/</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S2</font> &amp; the <a href="msualg_1.html#U2">Arity</a> of <a href="msualg_1.html#G1">ManySortedSign</a>(# <font color="Maroon">CARR</font>,<span class="p1">(<span class="default">the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S1</font> <a href="xboole_0.html#K2">\/</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S2</font></span>)</span>,<font color="Maroon">ARITY</font>,<font color="Maroon">RESULT</font> #) <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S1</font> <a href="funct_4.html#K1">+*</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S2</font> &amp; the <a href="msualg_1.html#U3">ResultSort</a> of <a href="msualg_1.html#G1">ManySortedSign</a>(# <font color="Maroon">CARR</font>,<span class="p1">(<span class="default">the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S1</font> <a href="xboole_0.html#K2">\/</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S2</font></span>)</span>,<font color="Maroon">ARITY</font>,<font color="Maroon">RESULT</font> #) <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S1</font> <a href="funct_4.html#K1">+*</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S2</font> )
 ;<br/>


</div>
