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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be  non <a href="struct_0.html#V3">empty</a>  <a href="msualg_1.html#L1">ManySortedSign</a> ;<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>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>5</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>let </b><font color="Maroon">c<sub>6</sub></font> be    <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Maroon">c<sub>3</sub></font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:36"/><i><font color="Green">E23</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="circcomb.html#R1" target="_self">tolerates</a> <font color="Maroon">c<sub>2</sub></font> &amp; the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>4</sub></font> <a href="partfun1.html#R1">tolerates</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>5</sub></font> &amp; the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">c<sub>4</sub></font> <a href="partfun1.html#R1">tolerates</a> the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">c<sub>5</sub></font> )
 <b>and </b><br/><a NAME="E2:36"/><i><font color="Green">E24</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="circcomb.html#R1" target="_self">tolerates</a> <font color="Maroon">c<sub>3</sub></font> &amp; the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>5</sub></font> <a href="partfun1.html#R1">tolerates</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>6</sub></font> &amp; the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">c<sub>5</sub></font> <a href="partfun1.html#R1">tolerates</a> the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">c<sub>6</sub></font> )
 <b>and </b><br/><a NAME="E3:36"/><i><font color="Green">E25</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="circcomb.html#R1" target="_self">tolerates</a> <font color="Maroon">c<sub>1</sub></font> &amp; the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>6</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> &amp; the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">c<sub>6</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> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="circcomb.html#D3" target="_self">CIRCCOMB:def 3</a><br/>

<b>thus </b><a NAME="E4:36"/>
<font color="Maroon">c<sub>1</sub></font> <a href="circcomb.html#K3" target="_self">+*</a> <font color="Maroon">c<sub>2</sub></font> <a href="circcomb.html#R1" target="_self">tolerates</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="circcomb.html#E1:36"><i><font color="Green">E23</font></i></a>, <a class="txt" href="circcomb.html#E2:36"><i><font color="Green">E24</font></i></a>, <a class="txt" href="circcomb.html#E3:36"><i><font color="Green">E25</font></i></a>, <a class="ref" href="circcomb.html#T7" target="_self">Th7</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="circcomb.html#D3" target="_self">CIRCCOMB:def 3</a><br/>

<a NAME="E5:36"/>
the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="circcomb.html#K4" target="_self">+*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>4</sub></font> <a href="circcomb.html#K1" target="_self">+*</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="circcomb.html#E1:36"><i><font color="Green">E23</font></i></a>, <a class="ref" href="circcomb.html#D4" target="_self">Def4</a></i>;<br/>
<b>hence </b><a NAME="E6:36"/>
the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="circcomb.html#K4" target="_self">+*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partfun1.html#R1">tolerates</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="circcomb.html#E1:36"><i><font color="Green">E23</font></i></a>, <a class="txt" href="circcomb.html#E2:36"><i><font color="Green">E24</font></i></a>, <a class="txt" href="circcomb.html#E3:36"><i><font color="Green">E25</font></i></a>, <a class="ref" href="circcomb.html#T5" target="_self">Th5</a></i>;<br/>

<a NAME="E7:36"/>
the <a href="msualg_1.html#U5">Charact</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="circcomb.html#K4" target="_self">+*</a> <font color="Maroon">c<sub>5</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>4</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>5</sub></font>
 
<b>by </b><i><a class="txt" href="circcomb.html#E1:36"><i><font color="Green">E23</font></i></a>, <a class="ref" href="circcomb.html#D4" target="_self">Def4</a></i>;<br/>
<b>hence </b><a NAME="E8:36"/>
the <a href="msualg_1.html#U5">Charact</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="circcomb.html#K4" target="_self">+*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partfun1.html#R1">tolerates</a> the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="circcomb.html#E1:36"><i><font color="Green">E23</font></i></a>, <a class="txt" href="circcomb.html#E2:36"><i><font color="Green">E24</font></i></a>, <a class="txt" href="circcomb.html#E3:36"><i><font color="Green">E25</font></i></a>, <a class="ref" href="circcomb.html#T5" target="_self">Th5</a></i>;<br/>


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