<?xml version="1.0"?>
<div class="add">

<b>set </b><font color="Maroon">S</font> = <font color="Maroon">S1</font> <a href="circcomb.html#K3" target="_self">+*</a> <font color="Maroon">S2</font>;<br/>
<a NAME="E1:33_1_1"/><i><font color="Green">E33</font></i>: 
( the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">S1</font> <a href="circcomb.html#K3" target="_self">+*</a> <font color="Maroon">S2</font></span>)</span> <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 <span class="p1">(<span class="default"><font color="Maroon">S1</font> <a href="circcomb.html#K3" target="_self">+*</a> <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; the <a href="msualg_1.html#U2">Arity</a> of <span class="p1">(<span class="default"><font color="Maroon">S1</font> <a href="circcomb.html#K3" target="_self">+*</a> <font color="Maroon">S2</font></span>)</span> <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 <span class="p1">(<span class="default"><font color="Maroon">S1</font> <a href="circcomb.html#K3" target="_self">+*</a> <font color="Maroon">S2</font></span>)</span> <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> )
 
<b>by </b><i/>;<br/>
<b>reconsider </b><font color="Maroon">SORTS</font> = the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A1</font> <a href="circcomb.html#K1" target="_self">+*</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A2</font> as  <a href="relat_1.html#V2">V3</a>  <a href="pboole.html#M1">ManySortedSet</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">S1</font> <a href="circcomb.html#K3" target="_self">+*</a> <font color="Maroon">S2</font></span>)</span> <b>by </b><i/>;<br/>
<b>set </b><font color="Maroon">SA1</font> = the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A1</font>;<br/>
<b>set </b><font color="Maroon">SA2</font> = the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A2</font>;<br/>
<b>set </b><font color="Maroon">I</font> = the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">S1</font> <a href="circcomb.html#K3" target="_self">+*</a> <font color="Maroon">S2</font></span>)</span>;<br/>
<b>set </b><font color="Maroon">I1</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S1</font>;<br/>
<b>set </b><font color="Maroon">I2</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S2</font>;<br/>
<b>set </b><font color="Maroon">SA12</font> = <span class="p1">(<span class="default">the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A1</font> <a href="pboole.html#K6">#</a> </span>)</span> <a href="circcomb.html#K1" target="_self">+*</a> <span class="p1">(<span class="default">the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A2</font> <a href="pboole.html#K6">#</a> </span>)</span>;<br/>
<b>set </b><font color="Maroon">CHARACT</font> = the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">A1</font> <a href="circcomb.html#K2" target="_self">+*</a> the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">A2</font>;<br/>
<a NAME="E3:33_1_1"/><i><font color="Green">E38</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default">the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A1</font> <a href="pboole.html#K6">#</a> </span>)</span> <a href="hidden.html#R1">=</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#K1">dom</a> <span class="p1">(<span class="default">the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A2</font> <a href="pboole.html#K6">#</a> </span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S2</font> <a href="finseq_2.html#K3">*</a>  &amp;  <a href="relat_1.html#K1">dom</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A1</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S1</font> &amp;  <a href="relat_1.html#K1">dom</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A2</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S2</font> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">SORTS</font> <a href="pboole.html#K6">#</a> </span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">S1</font> <a href="circcomb.html#K3" target="_self">+*</a> <font color="Maroon">S2</font></span>)</span> <a href="finseq_2.html#K3">*</a>  &amp;  <a href="relat_1.html#K1">dom</a> <font color="Maroon">SORTS</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">S1</font> <a href="circcomb.html#K3" target="_self">+*</a> <font color="Maroon">S2</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/>
<a NAME="E4:33_1_1"/><i><font color="Green">E42</font></i>: 
(  <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>  &amp;  <a href="relat_1.html#K2">rng</a> the <a href="msualg_1.html#U2">Arity</a> of <span class="p1">(<span class="default"><font color="Maroon">S1</font> <a href="circcomb.html#K3" target="_self">+*</a> <font color="Maroon">S2</font></span>)</span> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">S1</font> <a href="circcomb.html#K3" target="_self">+*</a> <font color="Maroon">S2</font></span>)</span> <a href="finseq_2.html#K3">*</a>  &amp;  <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> )
 
<b>by </b><i><a class="ref" href="relset_1.html#T12">RELSET_1:12</a></i>;<br/>
<a NAME="E5:33_1_1"/><b>then </b><i><font color="Green">E43</font></i>: 
<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> <span class="p1">(<span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S1</font> <a href="finseq_2.html#K3">*</a> </span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S2</font> <a href="finseq_2.html#K3">*</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T13">XBOOLE_1:13</a></i>;<br/>
<a NAME="E6:33_1_1"/>
<font color="Maroon">SORTS</font> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A1</font> <a href="xboole_0.html#K2">\/</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A2</font>
 
<b>by </b><i>, <a class="ref" href="funct_4.html#T31">FUNCT_4:31</a></i>;<br/>
<a NAME="E7:33_1_1"/><b>then </b><i><font color="Green">E45</font></i>: 
( the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">SORTS</font> &amp; the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A2</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">SORTS</font> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E8:33_1_1"/><i><font color="Green">E75</font></i>: 
the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A1</font> <a href="pboole.html#K6">#</a>  <a href="partfun1.html#R1">tolerates</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A2</font> <a href="pboole.html#K6">#</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="33_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="partfun1.html#D6">PARTFUN1:def 6</a><br/>

<b>assume </b><a NAME="E1:33_1_1_1"/><i><font color="Green">E78</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default">the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A1</font> <a href="pboole.html#K6">#</a> </span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default">the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A2</font> <a href="pboole.html#K6">#</a> </span>)</span></span>)</span>
 ;<br/>

<b>then reconsider </b><font color="Maroon">i1</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">S1</font> <a href="finseq_2.html#K3">*</a>  <b>by </b><i>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<b>reconsider </b><font color="Maroon">i2</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">S2</font> <a href="finseq_2.html#K3">*</a>  <b>by </b><i>, , <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E4:33_1_1_1"/><i><font color="Green">E107</font></i>: 
(  <a href="relat_1.html#K2">rng</a> <font color="Maroon">i1</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> <font color="Maroon">i2</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S2</font> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default">the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A1</font> <a href="pboole.html#K6">#</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
 <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default">the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A1</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">i1</font></span>)</span>
<b>by </b><i><a class="ref" href="pboole.html#D19">PBOOLE:def 19</a></i>
<br/>.= 
 <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default">the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A2</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">i2</font></span>)</span>
<b>by </b><i>, , <a class="txt" href="circcomb.html#E2"><i><font color="Green">Lemma29</font></i></a>, </i>
<br/>.= 
<span class="p1">(<span class="default">the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A2</font> <a href="pboole.html#K6">#</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="pboole.html#D19">PBOOLE:def 19</a></i>
;<br/>


</div><b>end;</b></div>
<a NAME="E9:33_1_1"/><b>then </b>
( <span class="p1">(<span class="default">the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A1</font> <a href="pboole.html#K6">#</a> </span>)</span> <a href="circcomb.html#K1" target="_self">+*</a> <span class="p1">(<span class="default">the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A2</font> <a href="pboole.html#K6">#</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A1</font> <a href="pboole.html#K6">#</a> </span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default">the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A2</font> <a href="pboole.html#K6">#</a> </span>)</span> &amp; the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A1</font> <a href="pboole.html#K6">#</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">SORTS</font> <a href="pboole.html#K6">#</a>  &amp; the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A2</font> <a href="pboole.html#K6">#</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">SORTS</font> <a href="pboole.html#K6">#</a>  )
 
<b>by </b><i><a class="txt" href="circcomb.html#E1"><i><font color="Green">Lemma26</font></i></a>, , <a class="ref" href="funct_4.html#T31">FUNCT_4:31</a></i>;<br/>
<a NAME="E10:33_1_1"/><b>then </b>
<span class="p1">(<span class="default">the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A1</font> <a href="pboole.html#K6">#</a> </span>)</span> <a href="circcomb.html#K1" target="_self">+*</a> <span class="p1">(<span class="default">the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A2</font> <a href="pboole.html#K6">#</a> </span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">SORTS</font> <a href="pboole.html#K6">#</a> 
 
<b>by </b><i><a class="ref" href="xboole_1.html#T8">XBOOLE_1:8</a></i>;<br/>
<a NAME="E11:33_1_1"/><b>then </b><i><font color="Green">E108</font></i>: 
<span class="p1">(<span class="default">the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A1</font> <a href="pboole.html#K6">#</a> </span>)</span> <a href="circcomb.html#K1" target="_self">+*</a> <span class="p1">(<span class="default">the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A2</font> <a href="pboole.html#K6">#</a> </span>)</span> <a href="partfun1.html#R1">tolerates</a> <font color="Maroon">SORTS</font> <a href="pboole.html#K6">#</a> 
 
<b>by </b><i><a class="ref" href="partfun1.html#T135">PARTFUN1:135</a></i>;<br/>
<a NAME="E12:33_1_1"/>
(  <a href="relat_1.html#K2">rng</a> the <a href="msualg_1.html#U2">Arity</a> of <span class="p1">(<span class="default"><font color="Maroon">S1</font> <a href="circcomb.html#K3" target="_self">+*</a> <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;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A1</font> <a href="pboole.html#K6">#</a> </span>)</span> <a href="circcomb.html#K1" target="_self">+*</a> <span class="p2">(<span class="default">the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A2</font> <a href="pboole.html#K6">#</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S1</font> <a href="finseq_2.html#K3">*</a> </span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S2</font> <a href="finseq_2.html#K3">*</a> </span>)</span> )
 
<b>by </b><i>, <a class="ref" href="funct_4.html#T18">FUNCT_4:18</a>, <a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/>
<a NAME="E13:33_1_1"/><b>then </b><i><font color="Green">E109</font></i>: 
 <a href="relat_1.html#K2">rng</a> the <a href="msualg_1.html#U2">Arity</a> of <span class="p1">(<span class="default"><font color="Maroon">S1</font> <a href="circcomb.html#K3" target="_self">+*</a> <font color="Maroon">S2</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A1</font> <a href="pboole.html#K6">#</a> </span>)</span> <a href="circcomb.html#K1" target="_self">+*</a> <span class="p2">(<span class="default">the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A2</font> <a href="pboole.html#K6">#</a> </span>)</span></span>)</span>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E14:33_1_1"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A1</font> <a href="pboole.html#K6">#</a> </span>)</span> <a href="circcomb.html#K1" target="_self">+*</a> <span class="p2">(<span class="default">the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A2</font> <a href="pboole.html#K6">#</a> </span>)</span></span>)</span> <a href="funct_1.html#NK3" target="_self">*</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> <span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A1</font> <a href="pboole.html#K6">#</a> </span>)</span> <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S1</font></span>)</span> <a href="circcomb.html#K1" target="_self">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A2</font> <a href="pboole.html#K6">#</a> </span>)</span> <a href="pboole.html#K7">*</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">the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A1</font> <a href="circcomb.html#K1" target="_self">+*</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A2</font></span>)</span> <a href="funct_1.html#NK3" target="_self">*</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> <span class="p1">(<span class="default">the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A1</font> <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S1</font></span>)</span> <a href="circcomb.html#K1" target="_self">+*</a> <span class="p1">(<span class="default">the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A2</font> <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S2</font></span>)</span> )
 
<b>by </b><i>, , <a class="txt" href="circcomb.html#E1:33"><i><font color="Green">E24</font></i></a>, , <a class="ref" href="funct_4.html#T73">FUNCT_4:73</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">CHARACT</font> = the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">A1</font> <a href="circcomb.html#K2" target="_self">+*</a> the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">A2</font> as    <a href="pboole.html#M3">ManySortedFunction</a> of <span class="p1">(<span class="default"><font color="Maroon">SORTS</font> <a href="pboole.html#K6">#</a> </span>)</span> <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U2">Arity</a> of <span class="p1">(<span class="default"><font color="Maroon">S1</font> <a href="circcomb.html#K3" target="_self">+*</a> <font color="Maroon">S2</font></span>)</span>,<font color="Maroon">SORTS</font> <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U3">ResultSort</a> of <span class="p1">(<span class="default"><font color="Maroon">S1</font> <a href="circcomb.html#K3" target="_self">+*</a> <font color="Maroon">S2</font></span>)</span> <b>by </b><i>, , <a class="txt" href="circcomb.html#E1:33"><i><font color="Green">E24</font></i></a>, , <a class="txt" href="circcomb.html#E2"><i><font color="Green">Lemma29</font></i></a>, </i>;<br/>
<b>reconsider </b><font color="Maroon">A</font> =  <a href="msualg_1.html#G3">MSAlgebra</a>(# <font color="Maroon">SORTS</font>,<font color="Maroon">CHARACT</font> #) as  <a href="msualg_1.html#V4">strict</a> <a href="msualg_1.html#V5">non-empty</a>  <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Maroon">S1</font> <a href="circcomb.html#K3" target="_self">+*</a> <font color="Maroon">S2</font> <b>by </b><i><a class="ref" href="msualg_1.html#D8">MSUALG_1:def 8</a></i>;<br/>
<b>take </b>
<font color="Maroon">A</font>
;<br/>

<b>thus </b><a NAME="E17:33_1_1"/>
( the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A1</font> <a href="circcomb.html#K1" target="_self">+*</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A2</font> &amp; the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">A1</font> <a href="circcomb.html#K2" target="_self">+*</a> the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">A2</font> )
 ;<br/>


</div>
