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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> 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>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> = the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>4</sub></font> =  <a href="msualg_3.html#K2">id</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="autalg_1.html#K6" target="_self">MSAAutGroup</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <b>by </b><i><a class="ref" href="autalg_1.html#T31" target="_self">Th31</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>5</sub></font> being    <a href="pboole.html#M3">ManySortedFunction</a> of the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font><b> such that </b><br/><a NAME="E3:44"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>
<b>consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="autalg_1.html#K6" target="_self">MSAAutGroup</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>;<br/>
<a NAME="E5:44"/>
<font color="Maroon">c<sub>6</sub></font> is    <a href="autalg_1.html#M2" target="_self">Element</a> of  <a href="autalg_1.html#K4" target="_self">MSAAut</a> <font color="Maroon">c<sub>2</sub></font>
 
;<br/>
<b>then consider </b><font color="Maroon">c<sub>7</sub></font> being    <a href="pboole.html#M3">ManySortedFunction</a> of the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font><b> such that </b><br/><a NAME="E7:44"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/>
<font color="Maroon">c<sub>4</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></font> = 
<font color="Maroon">c<sub>7</sub></font> <a href="msualg_3.html#K3">**</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="autalg_1.html#E3:44"><i><font color="Green">E30</font></i></a>, <a class="txt" href="autalg_1.html#E7:44"><i><font color="Green">E31</font></i></a>, <a class="ref" href="autalg_1.html#T35" target="_self">Th35</a></i>
<br/>.= 
<font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="txt" href="autalg_1.html#E3:44"><i><font color="Green">E30</font></i></a>, <a class="txt" href="autalg_1.html#E7:44"><i><font color="Green">E31</font></i></a>, <a class="ref" href="msualg_3.html#T3">MSUALG_3:3</a></i>
;<br/>
<b>hence </b><a NAME="E9:44"/>
 <a href="msualg_3.html#K2">id</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <span class="p1">(<span class="default"><a href="autalg_1.html#K6" target="_self">MSAAutGroup</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="group_1.html#T15">GROUP_1:15</a></i>;<br/>


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