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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="msualg_1.html#V1">strict</a>  <a href="msualg_1.html#L1">ManySortedSign</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  <a href="msualg_1.html#V5">non-empty</a>  <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>set </b><font color="Maroon">c<sub>3</sub></font> =  <a href="msualg_1.html#G3">MSAlgebra</a>(# the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">c<sub>2</sub></font> #);<br/>
<b>set </b><font color="Maroon">c<sub>4</sub></font> = the <a href="msualg_1.html#U4">Sorts</a> of <a href="msualg_1.html#G3">MSAlgebra</a>(# the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">c<sub>2</sub></font> #);<br/>
<b>set </b><font color="Maroon">c<sub>5</sub></font> = the <a href="msualg_1.html#U5">Charact</a> of <a href="msualg_1.html#G3">MSAlgebra</a>(# the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">c<sub>2</sub></font> #);<br/>
<b>set </b><font color="Maroon">c<sub>6</sub></font> = the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="circcomb.html#K4" target="_self">+*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>7</sub></font> = the <a href="msualg_1.html#U5">Charact</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="circcomb.html#K4" target="_self">+*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>;<br/>
<a NAME="E1:37"/>
( the <a href="msualg_1.html#U4">Sorts</a> of <a href="msualg_1.html#G3">MSAlgebra</a>(# the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">c<sub>2</sub></font> #) <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U4">Sorts</a> of <a href="msualg_1.html#G3">MSAlgebra</a>(# the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">c<sub>2</sub></font> #) <a href="circcomb.html#K1" target="_self">+*</a> the <a href="msualg_1.html#U4">Sorts</a> of <a href="msualg_1.html#G3">MSAlgebra</a>(# the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">c<sub>2</sub></font> #) &amp; the <a href="msualg_1.html#U5">Charact</a> of <a href="msualg_1.html#G3">MSAlgebra</a>(# the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">c<sub>2</sub></font> #) <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U5">Charact</a> of <a href="msualg_1.html#G3">MSAlgebra</a>(# the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">c<sub>2</sub></font> #) <a href="circcomb.html#K1" target="_self">+*</a> the <a href="msualg_1.html#U5">Charact</a> of <a href="msualg_1.html#G3">MSAlgebra</a>(# the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">c<sub>2</sub></font> #) )
 
;<br/>
<a NAME="E2:37"/><b>then </b>
( <font color="Maroon">c<sub>2</sub></font> <a href="circcomb.html#K4" target="_self">+*</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="msualg_1.html#G3">MSAlgebra</a>(# the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="circcomb.html#K4" target="_self">+*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,the <a href="msualg_1.html#U5">Charact</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="circcomb.html#K4" target="_self">+*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> #) &amp;  <a href="msualg_1.html#G3">MSAlgebra</a>(# the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">c<sub>2</sub></font> #) <a href="hidden.html#R1">=</a>  <a href="msualg_1.html#G3">MSAlgebra</a>(# the <a href="msualg_1.html#U4">Sorts</a> of <a href="msualg_1.html#G3">MSAlgebra</a>(# the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">c<sub>2</sub></font> #),the <a href="msualg_1.html#U5">Charact</a> of <a href="msualg_1.html#G3">MSAlgebra</a>(# the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">c<sub>2</sub></font> #) #) &amp; <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="circcomb.html#K3" target="_self">+*</a> <font color="Maroon">c<sub>1</sub></font> &amp; the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="circcomb.html#K4" target="_self">+*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U4">Sorts</a> of <a href="msualg_1.html#G3">MSAlgebra</a>(# the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">c<sub>2</sub></font> #) &amp; the <a href="msualg_1.html#U5">Charact</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="circcomb.html#K4" target="_self">+*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U5">Charact</a> of <a href="msualg_1.html#G3">MSAlgebra</a>(# the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">c<sub>2</sub></font> #) )
 
<b>by </b><i><a class="ref" href="circcomb.html#D4" target="_self">Def4</a>, <a class="ref" href="circcomb.html#T8" target="_self">Th8</a></i>;<br/>
<b>hence </b><a NAME="E3:37"/>
<font color="Maroon">c<sub>2</sub></font> <a href="circcomb.html#K4" target="_self">+*</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="msualg_1.html#G3">MSAlgebra</a>(# the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">c<sub>2</sub></font> #)
 ;<br/>


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