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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>let </b><font color="Maroon">c<sub>3</sub></font> be    <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>let </b><font color="Maroon">c<sub>4</sub></font> be   <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/>







<b>assume </b><a NAME="E1:45"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">c<sub>3</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>5</sub></font> being    <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><b> such that </b><br/><a NAME="E3:45"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="group_1.html#K3">"</a> 
 ;<br/>
<a NAME="E4:45"/><i><font color="Green">E32</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> is <a href="msualg_3.html#V1">"1-1"</a> &amp; <font color="Maroon">c<sub>3</sub></font> is <a href="msualg_3.html#V2">"onto"</a> )
 
<b>by </b><i><a class="txt" href="autalg_1.html#E40"><i><font color="Green">Lemma22</font></i></a></i>;<br/>
<a NAME="E5:45"/>
<font color="Maroon">c<sub>5</sub></font> <a href="msualg_3.html#K3">**</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="group_1.html#K3">"</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="autalg_1.html#E1:45"><i><font color="Green">E30</font></i></a>, <a class="txt" href="autalg_1.html#E3:45"><i><font color="Green">E31</font></i></a>, <a class="ref" href="autalg_1.html#T35" target="_self">Th35</a></i>;<br/>
<a NAME="E6:45"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="msualg_3.html#K3">**</a> <font color="Maroon">c<sub>3</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#D6">GROUP_1:def 6</a></i>;<br/>
<a NAME="E7:45"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="msualg_3.html#K3">**</a> <font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#R6">=</a>  <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>
 
<b>by </b><i><a class="ref" href="autalg_1.html#T36" target="_self">Th36</a></i>;<br/>
<b>hence </b><a NAME="E8:45"/>
<font color="Maroon">c<sub>3</sub></font> <a href="msualg_3.html#K4">""</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="group_1.html#K3">"</a> 
 <b>by </b><i><a class="txt" href="autalg_1.html#E3:45"><i><font color="Green">E31</font></i></a>, <a class="txt" href="autalg_1.html#E4:45"><i><font color="Green">E32</font></i></a>, <a class="ref" href="autalg_1.html#T19" target="_self">Th19</a></i>;<br/>


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