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

<span class="kw">set </span><font color="Maroon" title="c3">RESULT</font> = the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c1">S1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c2">S2</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">ARITY</font> = the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c1">S1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c2">S2</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">OPER</font> = the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">S1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">S2</font>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c6">CARR</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S2</font> as  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  ;<br/>
<a NAME="E2:16_1_1"/><span class="lab"><font color="Green" title="E7">A1</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c2">S2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">S2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E3:16_1_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c1">S1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">S1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E4:16_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E8">A2</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default">the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c1">S1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c2">S2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">S1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">S2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:16_1_1"><span class="lab"><font color="Green" title="E7">A1</font></span></a>, <a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></span>;<br/>
<a NAME="E5:16_1_1"/><span class="lab"><font color="Green" title="E9">A3</font></span>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">CARR</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></span>;<br/>
<a NAME="E6:16_1_1"/><span class="lab"><font color="Green" title="E10">A4</font></span>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">CARR</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></span>;<br/>
<a NAME="E7:16_1_1"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c2">S2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D19" title="RELAT_1:def.19">RELAT_1:def 19</a></span>;<br/>
<a NAME="E8:16_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E11">A5</font></span>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c2">S2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">CARR</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:16_1_1"><span class="lab"><font color="Green" title="E10">A4</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/>
<a NAME="E9:16_1_1"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c1">S1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D19" title="RELAT_1:def.19">RELAT_1:def 19</a></span>;<br/>
<a NAME="E10:16_1_1"/><span class="kw">then </span>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c1">S1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">CARR</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:16_1_1"><span class="lab"><font color="Green" title="E9">A3</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/>
<a NAME="E11:16_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E12">A6</font></span>: 
<span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c1">S1</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c2">S2</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">CARR</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:16_1_1"><span class="lab"><font color="Green" title="E11">A5</font></span></a>, <a class="ref" href="xboole_1.html#T8" title="XBOOLE_1:th.8">XBOOLE_1:8</a></span>;<br/>
<a NAME="E12:16_1_1"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default">the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c1">S1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c2">S2</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c1">S1</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c2">S2</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T18" title="FUNCT_4:th.18">FUNCT_4:18</a></span>;<br/>
<a NAME="E13:16_1_1"/><span class="kw">then </span>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default">the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c1">S1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c2">S2</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">CARR</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:16_1_1"><span class="lab"><font color="Green" title="E12">A6</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c7">RESULT</font> = the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c1">S1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c2">S2</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default">the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">S1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">S2</font></span>)</span>,<font color="Maroon" title="c6">CARR</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:16_1_1"><span class="lab"><font color="Green" title="E8">A2</font></span></a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a>, <a class="ref" href="relset_1.html#T11" title="RELSET_1:th.11">RELSET_1:11</a></span>;<br/>
<a NAME="E15:16_1_1"/><span class="lab"><font color="Green" title="E13">A7</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c2">S2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">S2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E16:16_1_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c1">S1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">S1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E17:16_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E14">A8</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default">the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c1">S1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c2">S2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">S1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">S2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:16_1_1"><span class="lab"><font color="Green" title="E13">A7</font></span></a>, <a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></span>;<br/>
<a NAME="E18:16_1_1"/><span class="lab"><font color="Green" title="E15">A9</font></span>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c1">S1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S1</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D19" title="RELAT_1:def.19">RELAT_1:def 19</a></span>;<br/>
<a NAME="E19:16_1_1"/><span class="lab"><font color="Green" title="E16">A10</font></span>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c2">S2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S2</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D19" title="RELAT_1:def.19">RELAT_1:def 19</a></span>;<br/>
<a NAME="E20:16_1_1"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S2</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">CARR</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T83" title="FINSEQ_1:th.83">FINSEQ_1:83</a>, <a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></span>;<br/>
<a NAME="E21:16_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E17">A11</font></span>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c2">S2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">CARR</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:16_1_1"><span class="lab"><font color="Green" title="E16">A10</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/>
<a NAME="E22:16_1_1"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S1</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">CARR</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T83" title="FINSEQ_1:th.83">FINSEQ_1:83</a>, <a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></span>;<br/>
<a NAME="E23:16_1_1"/><span class="kw">then </span>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c1">S1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">CARR</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:16_1_1"><span class="lab"><font color="Green" title="E15">A9</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/>
<a NAME="E24:16_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E18">A12</font></span>: 
<span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c1">S1</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c2">S2</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">CARR</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:16_1_1"><span class="lab"><font color="Green" title="E17">A11</font></span></a>, <a class="ref" href="xboole_1.html#T8" title="XBOOLE_1:th.8">XBOOLE_1:8</a></span>;<br/>
<a NAME="E25:16_1_1"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default">the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c1">S1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c2">S2</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c1">S1</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c2">S2</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T18" title="FUNCT_4:th.18">FUNCT_4:18</a></span>;<br/>
<a NAME="E26:16_1_1"/><span class="kw">then </span>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default">the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c1">S1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c2">S2</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">CARR</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:16_1_1"><span class="lab"><font color="Green" title="E18">A12</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c8">ARITY</font> = the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c1">S1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c2">S2</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default">the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">S1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">S2</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">CARR</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> </span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:16_1_1"><span class="lab"><font color="Green" title="E14">A8</font></span></a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a>, <a class="ref" href="relset_1.html#T11" title="RELSET_1:th.11">RELSET_1:11</a></span>;<br/>
<span class="kw">take </span>
 <a href="msualg_1.html#G1" title="MSUALG_1:aggr.1">ManySortedSign</a>(# <font color="Maroon" title="c6">CARR</font>,<span class="p1">(<span class="default">the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">S1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">S2</font></span>)</span>,<font color="Maroon" title="c8">ARITY</font>,<font color="Maroon" title="c7">RESULT</font> #)
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="msualg_1.html#G1" title="MSUALG_1:aggr.1">ManySortedSign</a>(# <font color="Maroon" title="c6">CARR</font>,<span class="p1">(<span class="default">the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">S1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">S2</font></span>)</span>,<font color="Maroon" title="c8">ARITY</font>,<font color="Maroon" title="c7">RESULT</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S2</font> &amp; the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <a href="msualg_1.html#G1" title="MSUALG_1:aggr.1">ManySortedSign</a>(# <font color="Maroon" title="c6">CARR</font>,<span class="p1">(<span class="default">the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">S1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">S2</font></span>)</span>,<font color="Maroon" title="c8">ARITY</font>,<font color="Maroon" title="c7">RESULT</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">S1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">S2</font> &amp; the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <a href="msualg_1.html#G1" title="MSUALG_1:aggr.1">ManySortedSign</a>(# <font color="Maroon" title="c6">CARR</font>,<span class="p1">(<span class="default">the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">S1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">S2</font></span>)</span>,<font color="Maroon" title="c8">ARITY</font>,<font color="Maroon" title="c7">RESULT</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c1">S1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c2">S2</font> &amp; the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <a href="msualg_1.html#G1" title="MSUALG_1:aggr.1">ManySortedSign</a>(# <font color="Maroon" title="c6">CARR</font>,<span class="p1">(<span class="default">the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">S1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">S2</font></span>)</span>,<font color="Maroon" title="c8">ARITY</font>,<font color="Maroon" title="c7">RESULT</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c1">S1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c2">S2</font> )</span><br/>

<span class="kw">thus </span><a NAME="E28:16_1_1"/>
( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="msualg_1.html#G1" title="MSUALG_1:aggr.1">ManySortedSign</a>(# <font color="Maroon" title="c6">CARR</font>,<span class="p1">(<span class="default">the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">S1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">S2</font></span>)</span>,<font color="Maroon" title="c8">ARITY</font>,<font color="Maroon" title="c7">RESULT</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S2</font> &amp; the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <a href="msualg_1.html#G1" title="MSUALG_1:aggr.1">ManySortedSign</a>(# <font color="Maroon" title="c6">CARR</font>,<span class="p1">(<span class="default">the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">S1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">S2</font></span>)</span>,<font color="Maroon" title="c8">ARITY</font>,<font color="Maroon" title="c7">RESULT</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">S1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">S2</font> &amp; the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <a href="msualg_1.html#G1" title="MSUALG_1:aggr.1">ManySortedSign</a>(# <font color="Maroon" title="c6">CARR</font>,<span class="p1">(<span class="default">the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">S1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">S2</font></span>)</span>,<font color="Maroon" title="c8">ARITY</font>,<font color="Maroon" title="c7">RESULT</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c1">S1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c2">S2</font> &amp; the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <a href="msualg_1.html#G1" title="MSUALG_1:aggr.1">ManySortedSign</a>(# <font color="Maroon" title="c6">CARR</font>,<span class="p1">(<span class="default">the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">S1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">S2</font></span>)</span>,<font color="Maroon" title="c8">ARITY</font>,<font color="Maroon" title="c7">RESULT</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c1">S1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c2">S2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
