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<b>let </b><font color="Maroon" title="c1">S</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">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>, <font color="Maroon" title="c3">U2</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>let </b><font color="Maroon" title="c4">F</font> be   <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <font color="Maroon" title="c2">U1</font>,<font color="Maroon" title="c3">U2</font>;<br/>





<b>assume </b><a NAME="E1:42"/><i><font color="Green" title="E32">A1</font></i>: 
<font color="Maroon" title="c4">F</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a> <font color="Maroon" title="c2">U1</font>,<font color="Maroon" title="c3">U2</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c5">G</font> = <font color="Maroon" title="c4">F</font> as   <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <font color="Maroon" title="c2">U1</font>,<span class="p1">(<span class="default"><a href="msualg_3.html#K7" title="MSUALG_3:func.7">Image</a> <font color="Maroon" title="c4">F</font></span>)</span> <b>by </b><i><a class="txt" href="msualg_3.html#E36"><i><font color="Green" title="E30">Lm3</font></i></a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c5">G</font>
;<br/>

<b>thus </b><a NAME="E3:42"/>
( <font color="Maroon" title="c4">F</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c5">G</font> &amp; <font color="Maroon" title="c5">G</font> <a href="msualg_3.html#R2" title="MSUALG_3:pred.2">is_epimorphism</a> <font color="Maroon" title="c2">U1</font>, <a href="msualg_3.html#K7" title="MSUALG_3:func.7">Image</a> <font color="Maroon" title="c4">F</font> )
 <b>by </b><i><a class="txt" href="msualg_3.html#E1:42"><i><font color="Green" title="E32">A1</font></i></a>, <a class="ref" href="msualg_3.html#T20" target="_self" title="MSUALG_3:th.20">Th20</a></i>;<br/>


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