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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">A1</font>, <font color="Maroon" title="c3">A2</font>, <font color="Maroon" title="c4">B1</font>, <font color="Maroon" title="c5">B2</font> be    <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c1">S</font>;<br/>



<b>assume </b><a NAME="E1:6"/><i><font color="Green" title="E5">A1</font></i>: 
(  <a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(# the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c2">A1</font>,the <a href="msualg_1.html#U5" title="MSUALG_1:sel.5">Charact</a> of <font color="Maroon" title="c2">A1</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(# the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c4">B1</font>,the <a href="msualg_1.html#U5" title="MSUALG_1:sel.5">Charact</a> of <font color="Maroon" title="c4">B1</font> #) &amp;  <a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(# the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c3">A2</font>,the <a href="msualg_1.html#U5" title="MSUALG_1:sel.5">Charact</a> of <font color="Maroon" title="c3">A2</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(# the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c5">B2</font>,the <a href="msualg_1.html#U5" title="MSUALG_1:sel.5">Charact</a> of <font color="Maroon" title="c5">B2</font> #) )
 ;<br/>

<b>let </b><font color="Maroon" title="c6">f</font> be   <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <font color="Maroon" title="c2">A1</font>,<font color="Maroon" title="c3">A2</font>;<br/><b>let </b><font color="Maroon" title="c7">g</font> be   <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <font color="Maroon" title="c4">B1</font>,<font color="Maroon" title="c5">B2</font>;<br/>



<b>assume </b><a NAME="E2:6"/><i><font color="Green" title="E6">A2</font></i>: 
<font color="Maroon" title="c6">f</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c7">g</font>
 ;<br/>

<b>let </b><font color="Maroon" title="c8">o</font> be   <a href="msualg_1.html#NM2" title="MSUALG_1:NM.2">OperSymbol</a> of <font color="Maroon" title="c1">S</font>;<br/>

<b>assume </b><a NAME="E3:6"/><i><font color="Green" title="E7">A3</font></i>: 
(  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <font color="Maroon" title="c8">o</font>,<font color="Maroon" title="c2">A1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <font color="Maroon" title="c8">o</font>,<font color="Maroon" title="c3">A2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 ;<br/>

<b>let </b><font color="Maroon" title="c9">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <font color="Maroon" title="c8">o</font>,<font color="Maroon" title="c2">A1</font>;<br/><b>let </b><font color="Maroon" title="c10">y</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <font color="Maroon" title="c8">o</font>,<font color="Maroon" title="c4">B1</font>;<br/>



<b>assume </b><a NAME="E4:6"/><i><font color="Green" title="E8">A4</font></i>: 
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">y</font>
 ;<br/>

<a NAME="E5:6"/>
<font color="Maroon" title="c6">f</font> <a href="msualg_3.html#K5" title="MSUALG_3:func.5">#</a> <font color="Maroon" title="c9">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="pralg_2.html#K2" title="PRALG_2:func.2">Frege</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p3">(<span class="default"><a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c8">o</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">x</font>
 
<b>by </b><i><a class="txt" href="instalg1.html#E3:6"><i><font color="Green" title="E7">A3</font></i></a>, <a class="ref" href="msualg_3.html#D7" title="MSUALG_3:def.7">MSUALG_3:def 7</a></i>;<br/>
<b>hence </b><a NAME="E6:6"/>
<font color="Maroon" title="c6">f</font> <a href="msualg_3.html#K5" title="MSUALG_3:func.5">#</a> <font color="Maroon" title="c9">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">g</font> <a href="msualg_3.html#K5" title="MSUALG_3:func.5">#</a> <font color="Maroon" title="c10">y</font>
 <b>by </b><i><a class="txt" href="instalg1.html#E1:6"><i><font color="Green" title="E5">A1</font></i></a>, <a class="txt" href="instalg1.html#E2:6"><i><font color="Green" title="E6">A2</font></i></a>, <a class="txt" href="instalg1.html#E3:6"><i><font color="Green" title="E7">A3</font></i></a>, <a class="txt" href="instalg1.html#E4:6"><i><font color="Green" title="E8">A4</font></i></a>, <a class="ref" href="msualg_3.html#D7" title="MSUALG_3:def.7">MSUALG_3:def 7</a></i>;<br/>


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