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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be  non <a href="struct_0.html#V3">empty</a> non <a href="msualg_1.html#V2">void</a>  <a href="msualg_1.html#L1">ManySortedSign</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</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>let </b><font color="Maroon">c<sub>4</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>2</sub></font>;<br/>





<b>assume </b><a NAME="E1:47"/>
the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>3</sub></font> <a href="partfun1.html#R1">tolerates</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<a NAME="E2:47"/><b>then </b><i><font color="Green">E29</font></i>: 
the <a href="msualg_1.html#U5">Charact</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="circcomb.html#K4" target="_self">+*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">c<sub>3</sub></font> <a href="circcomb.html#K2" target="_self">+*</a> the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="circcomb.html#D4" target="_self">Def4</a></i>;<br/>
<b>assume </b><a NAME="E3:47"/><i><font color="Green">E30</font></i>: 
the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">c<sub>3</sub></font> <a href="partfun1.html#R1">tolerates</a> the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<b>set </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="circcomb.html#K4" target="_self">+*</a> <font color="Maroon">c<sub>4</sub></font>;<br/>
<b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="msualg_1.html#NM2">OperSymbol</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="circcomb.html#K3" target="_self">+*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>;<br/><b>let </b><font color="Maroon">c<sub>7</sub></font> be   <a href="msualg_1.html#NM2">OperSymbol</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E4:47"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/>

<a NAME="E5:47"/><i><font color="Green">E32</font></i>: 
 <a href="relat_1.html#K1">dom</a> the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/>
<a NAME="E6:47"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="circcomb.html#E2"><i><font color="Green">Lemma2</font></i></a></i>;<br/>
<b>thus </b> <a href="msualg_1.html#K5">Den</a> <font color="Maroon">c<sub>6</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="circcomb.html#K4" target="_self">+*</a> <font color="Maroon">c<sub>4</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>3</sub></font> <a href="circcomb.html#K4" target="_self">+*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font>

<br/>.= 
the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="circcomb.html#E2:47"><i><font color="Green">E29</font></i></a>, <a class="txt" href="circcomb.html#E3:47"><i><font color="Green">E30</font></i></a>, <a class="txt" href="circcomb.html#E4:47"><i><font color="Green">E31</font></i></a>, <a class="txt" href="circcomb.html#E5:47"><i><font color="Green">E32</font></i></a>, <a class="txt" href="circcomb.html#E6:47"><i><font color="Green">E33</font></i></a>, <a class="ref" href="funct_4.html#T16">FUNCT_4:16</a></i>
<br/>.= 
 <a href="msualg_1.html#K5">Den</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font>

;<br/>


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