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<b>let </b><font color="Maroon">S</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">U1</font> be  <a href="msualg_1.html#V5">non-empty</a>  <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">U2</font> be  <a href="msualg_1.html#V5">non-empty</a>  <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">F</font> be   <a href="msualg_3.html#NM1">ManySortedFunction</a> of <font color="Maroon">U1</font>,<font color="Maroon">U2</font>;<br/>







<b>assume </b><a NAME="E1:17"/>
<font color="Maroon">F</font> <a href="msualg_3.html#R1">is_homomorphism</a> <font color="Maroon">U1</font>,<font color="Maroon">U2</font>
 ;<br/>

<b>assume </b><a NAME="E2:17"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">F</font> <a href="msualg_3.html#R2">is_epimorphism</a> <font color="Maroon">U1</font>,<font color="Maroon">U2</font>
 ;<br/>

<b>let </b><font color="Maroon">U3</font> be  <a href="msualg_1.html#V5">non-empty</a>  <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">h1</font> be   <a href="msualg_3.html#NM1">ManySortedFunction</a> of <font color="Maroon">U2</font>,<font color="Maroon">U3</font>, <font color="Maroon">h2</font> be   <a href="msualg_3.html#NM1">ManySortedFunction</a> of <font color="Maroon">U2</font>,<font color="Maroon">U3</font>;<br/>



<b>assume </b><a NAME="E3:17"/>
( <font color="Maroon">h1</font> <a href="msualg_3.html#R1">is_homomorphism</a> <font color="Maroon">U2</font>,<font color="Maroon">U3</font> &amp; <font color="Maroon">h2</font> <a href="msualg_3.html#R1">is_homomorphism</a> <font color="Maroon">U2</font>,<font color="Maroon">U3</font> )
 ;<br/>

<b>assume </b><a NAME="E4:17"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">h1</font> <a href="msualg_3.html#K3">**</a> <font color="Maroon">F</font> <a href="pboole.html#R6">=</a> <font color="Maroon">h2</font> <a href="msualg_3.html#K3">**</a> <font color="Maroon">F</font>
 ;<br/>

<a NAME="E5:17"/>
<font color="Maroon">F</font> is <a href="msualg_3.html#V2">"onto"</a>
 
<b>by </b><i>, <a class="ref" href="msualg_3.html#D10">MSUALG_3:def 10</a></i>;<br/>
<b>hence </b><a NAME="E6:17"/>
<font color="Maroon">h1</font> <a href="pboole.html#R6">=</a> <font color="Maroon">h2</font>
 <b>by </b><i>, </i>;<br/>


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