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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="unialg_1.html#NM2">Universal_Algebra</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/>





<b>set </b><font color="Maroon">c<sub>4</sub></font> = <span class="p1">(<span class="default"><a href="msualg_1.html#K10">MSAlg</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="msuhom_1.html#K2" target="_self">Over</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K7">MSSign</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>5</sub></font> =  <a href="msuhom_1.html#K3" target="_self">MSAlg</a> <font color="Maroon">c<sub>3</sub></font>;<br/>
<b>assume </b><a NAME="E1:27"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="alg_1.html#R4">is_isomorphism</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E2:27"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="alg_1.html#R3">is_epimorphism</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="alg_1.html#D4">ALG_1:def 4</a></i>;<br/>
<b>hence </b><a NAME="E3:27"/>
 <a href="msuhom_1.html#K3" target="_self">MSAlg</a> <font color="Maroon">c<sub>3</sub></font> <a href="msualg_3.html#R2">is_epimorphism</a>  <a href="msualg_1.html#K10">MSAlg</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><a href="msualg_1.html#K10">MSAlg</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="msuhom_1.html#K2" target="_self">Over</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K7">MSSign</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="msuhom_1.html#T18" target="_self">Th18</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="msualg_3.html#D12">MSUALG_3:def 12</a><br/>

<a NAME="E4:27"/>
<font color="Maroon">c<sub>3</sub></font> <a href="alg_1.html#R2">is_monomorphism</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="msuhom_1.html#E1:27"><i><font color="Green">E22</font></i></a>, <a class="ref" href="alg_1.html#D4">ALG_1:def 4</a></i>;<br/>
<b>hence </b><a NAME="E5:27"/>
 <a href="msuhom_1.html#K3" target="_self">MSAlg</a> <font color="Maroon">c<sub>3</sub></font> <a href="msualg_3.html#R3">is_monomorphism</a>  <a href="msualg_1.html#K10">MSAlg</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><a href="msualg_1.html#K10">MSAlg</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="msuhom_1.html#K2" target="_self">Over</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K7">MSSign</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="msuhom_1.html#T19" target="_self">Th19</a></i>;<br/>


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