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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="osalg_1.html#NM3">OrderSortedSign</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be  <a href="msualg_1.html#V5">non-empty</a> <a href="osalg_1.html#NM5">OSAlgebra</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="msualg_3.html#NM1">ManySortedFunction</a> of <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>;<br/>





<b>assume </b><a NAME="E1:22"/><i><font color="Green">E16</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="msualg_3.html#R1">is_homomorphism</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> is <a href="osalg_3.html#V1" target="_self">order-sorted</a> )
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="msualg_3.html#NM1">ManySortedFunction</a> of <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="msualg_3.html#K7">Image</a> <font color="Maroon">c<sub>4</sub></font></span>)</span><b> such that </b><br/><a NAME="E3:22"/><i><font color="Green">E17</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="pboole.html#R6">=</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="msualg_3.html#R2">is_epimorphism</a> <font color="Maroon">c<sub>2</sub></font>, <a href="msualg_3.html#K7">Image</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="msualg_3.html#T21">MSUALG_3:21</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>5</sub></font>
;<br/>

<b>thus </b><a NAME="E4:22"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="pboole.html#R6">=</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> is <a href="osalg_3.html#V1" target="_self">order-sorted</a> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="msualg_3.html#R2">is_epimorphism</a> <font color="Maroon">c<sub>2</sub></font>, <a href="msualg_3.html#K7">Image</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="txt" href="osalg_3.html#E1:22"><i><font color="Green">E16</font></i></a>, <a class="txt" href="osalg_3.html#E3:22"><i><font color="Green">E17</font></i></a></i>;<br/>


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