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<b>let </b><font color="Maroon" title="c1">S</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> non <a href="msualg_1.html#V2" title="MSUALG_1:attr.2">void</a>  <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> ;<br/><b>let </b><font color="Maroon" title="c2">U1</font> be  <a href="msualg_1.html#V5" title="MSUALG_1:attr.5">non-empty</a>  <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c1">S</font>;<br/>



<b>set </b><font color="Maroon" title="c3">T</font> = the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c2">U1</font>;<br/>
<b>reconsider </b><font color="Maroon" title="c4">g</font> =  <a href="msualg_3.html#K2" title="MSUALG_3:func.2">id</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c2">U1</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="autalg_1.html#K6" title="AUTALG_1:func.6">MSAAutGroup</a> <font color="Maroon" title="c2">U1</font></span>)</span> <b>by </b><i><a class="ref" href="autalg_1.html#T31" target="_self" title="AUTALG_1:th.31">Th31</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c5">g1</font> being    <a href="pboole.html#M3" title="PBOOLE:mode.3">ManySortedFunction</a> of the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c2">U1</font>,the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c2">U1</font><b> such that </b><br/><a NAME="E3:44"/><i><font color="Green" title="E28">A1</font></i>: 
<font color="Maroon" title="c5">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">g</font>
 ;<br/>
<b>consider </b><font color="Maroon" title="c6">f</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="autalg_1.html#K6" title="AUTALG_1:func.6">MSAAutGroup</a> <font color="Maroon" title="c2">U1</font></span>)</span>;<br/>
<a NAME="E5:44"/>
<font color="Maroon" title="c6">f</font> is    <a href="autalg_1.html#M2" title="AUTALG_1:mode.2">Element</a> of  <a href="autalg_1.html#K4" title="AUTALG_1:func.4">MSAAut</a> <font color="Maroon" title="c2">U1</font>
 
;<br/>
<b>then consider </b><font color="Maroon" title="c7">f1</font> being    <a href="pboole.html#M3" title="PBOOLE:mode.3">ManySortedFunction</a> of the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c2">U1</font>,the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c2">U1</font><b> such that </b><br/><a NAME="E7:44"/><i><font color="Green" title="E29">A2</font></i>: 
<font color="Maroon" title="c7">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">f</font>
 ;<br/>
<font color="Maroon" title="c4">g</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c6">f</font> = 
<font color="Maroon" title="c7">f1</font> <a href="msualg_3.html#K3" title="MSUALG_3:func.3">**</a> <font color="Maroon" title="c5">g1</font>
<b>by </b><i><a class="txt" href="autalg_1.html#E3:44"><i><font color="Green" title="E28">A1</font></i></a>, <a class="txt" href="autalg_1.html#E7:44"><i><font color="Green" title="E29">A2</font></i></a>, <a class="ref" href="autalg_1.html#D8" target="_self" title="AUTALG_1:def.8">Def8</a></i>
<br/>.= 
<font color="Maroon" title="c6">f</font>
<b>by </b><i><a class="txt" href="autalg_1.html#E3:44"><i><font color="Green" title="E28">A1</font></i></a>, <a class="txt" href="autalg_1.html#E7:44"><i><font color="Green" title="E29">A2</font></i></a>, <a class="ref" href="msualg_3.html#T3" title="MSUALG_3:th.3">MSUALG_3:3</a></i>
;<br/>
<b>hence </b><a NAME="E9:44"/>
 <a href="msualg_3.html#K2" title="MSUALG_3:func.2">id</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c2">U1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <span class="p1">(<span class="default"><a href="autalg_1.html#K6" title="AUTALG_1:func.6">MSAAutGroup</a> <font color="Maroon" title="c2">U1</font></span>)</span>
 <b>by </b><i><a class="ref" href="group_1.html#T15" title="GROUP_1:th.15">GROUP_1:15</a></i>;<br/>


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