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<b>let </b><font color="Maroon" title="c1">S1</font>, <font color="Maroon" title="c2">S2</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a>  <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> ;<br/><b>let </b><font color="Maroon" title="c3">f</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S1</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S2</font>;<br/><b>let </b><font color="Maroon" title="c4">g</font> be   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>;<br/>





<b>assume </b><a NAME="E1:39"/><i><font color="Green" title="E22">A1</font></i>: 
<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">g</font> <a href="pua2mss1.html#R3" title="PUA2MSS1:pred.3">form_morphism_between</a> <font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c2">S2</font>
 ;<br/>

<b>let </b><font color="Maroon" title="c5">A1</font>, <font color="Maroon" title="c6">A2</font> be    <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c2">S2</font>;<br/><b>let </b><font color="Maroon" title="c7">h</font> be    <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="c5">A1</font>,the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c6">A2</font>;<br/>



<b>set </b><font color="Maroon" title="c8">B1</font> = <font color="Maroon" title="c5">A1</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">g</font>;<br/>
<b>set </b><font color="Maroon" title="c9">B2</font> = <font color="Maroon" title="c6">A2</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">g</font>;<br/>
<b>let </b><font color="Maroon" title="c10">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="pboole.html#D18" title="PBOOLE:def.18">PBOOLE:def 18</a><br/>

<b>assume </b><a NAME="E2:39"/>
<font color="Maroon" title="c10">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S1</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c11">s</font> = <font color="Maroon" title="c10">x</font> as   <a href="msualg_1.html#NM1" title="MSUALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c1">S1</font> ;<br/>
<b>reconsider </b><font color="Maroon" title="c12">fs</font> = <font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">s</font> as   <a href="msualg_1.html#NM1" title="MSUALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c2">S2</font> ;<br/>
<a NAME="E5:39"/>
( <span class="p1">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">h</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon" title="c12">fs</font> &amp; the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c5">A1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">fs</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c5">A1</font> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">s</font> &amp; the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c6">A2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">fs</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c6">A2</font> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">s</font> &amp; the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c5">A1</font> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> <font color="Maroon" title="c3">f</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c5">A1</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">g</font></span>)</span> &amp; the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c6">A2</font> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> <font color="Maroon" title="c3">f</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c6">A2</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">g</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="instalg1.html#E1:39"><i><font color="Green" title="E22">A1</font></i></a>, <a class="ref" href="instalg1.html#D3" target="_self" title="INSTALG1:def.3">Def3</a>, <a class="ref" href="funct_2.html#T21" title="FUNCT_2:th.21">FUNCT_2:21</a></i>;<br/>
<b>hence </b><a NAME="E6:39"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font> is   <a href="relset_1.html#M2" title="RELSET_1:mode.2">M6</a>(the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c5">A1</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">g</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font>,the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c6">A2</font> <a href="instalg1.html#K1" title="INSTALG1:func.1">|</a> <font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">g</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font>)
 ;<br/>


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