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<b>let </b><font color="Maroon">UA</font> be   <a href="unialg_1.html#NM2">Universal_Algebra</a>;<br/><b>let </b><font color="Maroon">F</font> be   <a href="msualg_3.html#NM1">ManySortedFunction</a> of <span class="p1">(<span class="default"><a href="msualg_1.html#K10">MSAlg</a> <font color="Maroon">UA</font></span>)</span>,<span class="p1">(<span class="default"><a href="msualg_1.html#K10">MSAlg</a> <font color="Maroon">UA</font></span>)</span>;<br/><b>let </b><font color="Maroon">f</font> be    <a href="fraenkel.html#M2">Element</a> of  <a href="endalg.html#K1" target="_self">UAEnd</a> <font color="Maroon">UA</font>;<br/>





<b>assume </b><a NAME="E1:16"/>
<font color="Maroon">F</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span> <a href="pboole.html#K9">--&gt;</a> <font color="Maroon">f</font>
 ;<br/>

<a NAME="E2:16"/><b>then </b><i><font color="Green">E32</font></i>: 
<font color="Maroon">F</font> <a href="pboole.html#R6">=</a>  <a href="msuhom_1.html#K3">MSAlg</a> <font color="Maroon">f</font>
 
<b>by </b><i><a class="ref" href="msuhom_1.html#D3">MSUHOM_1:def 3</a></i>;<br/>
<a NAME="E3:16"/>
<font color="Maroon">f</font> <a href="alg_1.html#R1">is_homomorphism</a> <font color="Maroon">UA</font>,<font color="Maroon">UA</font>
 
<b>by </b><i/>;<br/>
<a NAME="E4:16"/><b>then </b>
 <a href="msuhom_1.html#K3">MSAlg</a> <font color="Maroon">f</font> <a href="msualg_3.html#R1">is_homomorphism</a>  <a href="msualg_1.html#K10">MSAlg</a> <font color="Maroon">UA</font>,<span class="p1">(<span class="default"><a href="msualg_1.html#K10">MSAlg</a> <font color="Maroon">UA</font></span>)</span> <a href="msuhom_1.html#K2">Over</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K7">MSSign</a> <font color="Maroon">UA</font></span>)</span>
 
<b>by </b><i><a class="ref" href="msuhom_1.html#T16">MSUHOM_1:16</a></i>;<br/>
<a NAME="E5:16"/><b>then </b>
<font color="Maroon">F</font> <a href="msualg_3.html#R1">is_homomorphism</a>  <a href="msualg_1.html#K10">MSAlg</a> <font color="Maroon">UA</font>, <a href="msualg_1.html#K10">MSAlg</a> <font color="Maroon">UA</font>
 
<b>by </b><i>, <a class="ref" href="msuhom_1.html#T9">MSUHOM_1:9</a></i>;<br/>
<b>hence </b><a NAME="E6:16"/>
<font color="Maroon">F</font> <a href="hidden.html#R2">in</a>  <a href="endalg.html#K4" target="_self">MSAEnd</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K10">MSAlg</a> <font color="Maroon">UA</font></span>)</span>
 <b>by </b><i/>;<br/>


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