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<b>let </b><font color="Maroon" title="c1">S1</font>, <font color="Maroon" title="c2">S2</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a>  <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> ;<br/><b>let </b><font color="Maroon" title="c3">A1</font> be  <a href="circcomb.html#V6" title="CIRCCOMB:attr.6">Boolean</a>  <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c1">S1</font>;<br/><b>let </b><font color="Maroon" title="c4">A2</font> be  <a href="circcomb.html#V6" title="CIRCCOMB:attr.6">Boolean</a>  <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c2">S2</font>;<br/>





<b>set </b><font color="Maroon" title="c5">A</font> = <font color="Maroon" title="c3">A1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c4">A2</font>;<br/>
<b>set </b><font color="Maroon" title="c6">S</font> = <font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <font color="Maroon" title="c2">S2</font>;<br/>
<a NAME="E1:110"/><i><font color="Green" title="E62">A1</font></i>: 
( the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c3">A1</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</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="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <a href="circcomb.html#K10" title="CIRCCOMB:func.10">BOOLEAN</a>  &amp; the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c4">A2</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</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="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <a href="circcomb.html#K10" title="CIRCCOMB:func.10">BOOLEAN</a>  )
 
<b>by </b><i><a class="ref" href="circcomb.html#T65" target="_self" title="CIRCCOMB:th.65">Th65</a></i>;<br/>
<a NAME="E2:110"/><b>then </b><i><font color="Green" title="E63">A2</font></i>: 
the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c3">A1</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c4">A2</font>
 
<b>by </b><i><a class="ref" href="circcomb.html#T4" target="_self" title="CIRCCOMB:th.4">Th4</a></i>;<br/>
<a NAME="E3:110"/><b>then </b><i><font color="Green" title="E64">A3</font></i>: 
the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">A1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c4">A2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c3">A1</font> <a href="circcomb.html#K1" title="CIRCCOMB:func.1">+*</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c4">A2</font>
 
<b>by </b><i><a class="ref" href="circcomb.html#D4" target="_self" title="CIRCCOMB:def.4">Def4</a></i>;<br/>
<a NAME="E4:110"/><i><font color="Green" title="E65">A4</font></i>: 
(  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c3">A1</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> &amp;  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c4">A2</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="c2">S2</font> )
 
<b>by </b><i><a class="ref" href="pboole.html#D3" title="PBOOLE:def.3">PBOOLE:def 3</a></i>;<br/>
<b>let </b><font color="Maroon" title="c7">x</font> be   <a href="msafree2.html#NM1" title="MSAFREE2:NM.1">Vertex</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <font color="Maroon" title="c2">S2</font></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="circcomb.html#D15" target="_self" title="CIRCCOMB:def.15">CIRCCOMB:def 15</a><br/>

<a NAME="E5:110"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <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#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>
 
<b>by </b><i><a class="ref" href="circcomb.html#D2" target="_self" title="CIRCCOMB:def.2">Def2</a></i>;<br/>
<a NAME="E6:110"/><b>then </b>
( <font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S1</font> or <font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S2</font> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E7:110"/><b>then </b>
( ( the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">A1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c4">A2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c3">A1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font> &amp; the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c3">A1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="circcomb.html#K10" title="CIRCCOMB:func.10">BOOLEAN</a>  ) or ( the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">A1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c4">A2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c4">A2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font> &amp; the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c4">A2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="circcomb.html#K10" title="CIRCCOMB:func.10">BOOLEAN</a>  ) )
 
<b>by </b><i><a class="txt" href="circcomb.html#E1:110"><i><font color="Green" title="E62">A1</font></i></a>, <a class="txt" href="circcomb.html#E2:110"><i><font color="Green" title="E63">A2</font></i></a>, <a class="txt" href="circcomb.html#E3:110"><i><font color="Green" title="E64">A3</font></i></a>, <a class="txt" href="circcomb.html#E4:110"><i><font color="Green" title="E65">A4</font></i></a>, <a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a>, <a class="ref" href="funct_4.html#T16" title="FUNCT_4:th.16">FUNCT_4:16</a></i>;<br/>
<b>hence </b><a NAME="E8:110"/>
the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">A1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c4">A2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="circcomb.html#K10" title="CIRCCOMB:func.10">BOOLEAN</a> 
 ;<br/>


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