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<b>reconsider </b><font color="Maroon">SN</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">F<sub>1</sub></font>() <a href="pre_circ.html#K2">--&gt;</a> <a href="numbers.html#K5">NAT</a>  as  <a href="relat_1.html#V2">V5</a>  <a href="pboole.html#M1">ManySortedSet</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">F<sub>1</sub></font>() ;<br/>
<b>consider </b><font color="Maroon">H</font> being   <a href="msualg_3.html#NM1">ManySortedFunction</a> of <font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()<b> such that </b><br/><a NAME="E3:5_1"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">H</font> <a href="msualg_3.html#R1">is_homomorphism</a> <font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()
 <b>and </b><br/><a NAME="E4:5_1"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">F<sub>5</sub></font>() <a href="pboole.html#R6">=</a> <font color="Maroon">H</font> <a href="msualg_3.html#K3">**</a> <font color="Maroon">F<sub>4</sub></font>()
 <b>by </b><i>, </i>;<br/>
<b>reconsider </b><font color="Maroon">h1</font> = <font color="Maroon">F<sub>5</sub></font>() as    <a href="pboole.html#M3">ManySortedFunction</a> of <font color="Maroon">SN</font>,the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">F<sub>3</sub></font>() ;<br/>
<a NAME="E6:5_1"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">h1</font> <a href="birkhoff.html#K1" target="_self">-hash</a>  <a href="msualg_3.html#R1">is_homomorphism</a>  <a href="msafree.html#K11">FreeMSA</a> <font color="Maroon">SN</font>,<font color="Maroon">F<sub>3</sub></font>()
 
<b>by </b><i/>;<br/>
<a NAME="E7:5_1"/>
<font color="Maroon">F<sub>4</sub></font>() <a href="birkhoff.html#K1" target="_self">-hash</a>  <a href="msualg_3.html#R1">is_homomorphism</a>  <a href="msafree.html#K11">FreeMSA</a> <span class="p1">(<span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">F<sub>1</sub></font>() <a href="pre_circ.html#K2">--&gt;</a> <a href="numbers.html#K5">NAT</a> </span>)</span>,<font color="Maroon">F<sub>2</sub></font>()
 
<b>by </b><i/>;<br/>
<a NAME="E8:5_1"/><b>then </b><i><font color="Green">E64</font></i>: 
<font color="Maroon">H</font> <a href="msualg_3.html#K3">**</a> <span class="p1">(<span class="default"><font color="Maroon">F<sub>4</sub></font>() <a href="birkhoff.html#K1" target="_self">-hash</a> </span>)</span> <a href="msualg_3.html#R1">is_homomorphism</a>  <a href="msafree.html#K11">FreeMSA</a> <span class="p1">(<span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">F<sub>1</sub></font>() <a href="pre_circ.html#K2">--&gt;</a> <a href="numbers.html#K5">NAT</a> </span>)</span>,<font color="Maroon">F<sub>3</sub></font>()
 
<b>by </b><i>, <a class="ref" href="msualg_3.html#T10">MSUALG_3:10</a></i>;<br/>
<i><font color="Green">E67</font></i>: <span class="p1">(<span class="default"><font color="Maroon">h1</font> <a href="birkhoff.html#K1" target="_self">-hash</a> </span>)</span> <a href="msafree.html#K1">||</a> <span class="p1">(<span class="default"><a href="msafree.html#K13">FreeGen</a> <font color="Maroon">SN</font></span>)</span> = 
<font color="Maroon">F<sub>5</sub></font>() <a href="pboole.html#K12">**</a> <span class="p1">(<span class="default"><a href="msafree.html#K15">Reverse</a> <font color="Maroon">SN</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">H</font> <a href="pboole.html#K12">**</a> <span class="p1">(<span class="default"><font color="Maroon">F<sub>4</sub></font>() <a href="pboole.html#K12">**</a> <span class="p2">(<span class="default"><a href="msafree.html#K15">Reverse</a> <font color="Maroon">SN</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="autalg_1.html#T13">AUTALG_1:13</a></i>
<br/>.= 
<font color="Maroon">H</font> <a href="msualg_3.html#K3">**</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F<sub>4</sub></font>() <a href="birkhoff.html#K1" target="_self">-hash</a> </span>)</span> <a href="msafree.html#K1">||</a> <span class="p2">(<span class="default"><a href="msafree.html#K13">FreeGen</a> <span class="p3">(<span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">F<sub>1</sub></font>() <a href="pre_circ.html#K2">--&gt;</a> <a href="numbers.html#K5">NAT</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">H</font> <a href="msualg_3.html#K3">**</a> <span class="p2">(<span class="default"><font color="Maroon">F<sub>4</sub></font>() <a href="birkhoff.html#K1" target="_self">-hash</a> </span>)</span></span>)</span> <a href="msafree.html#K1">||</a> <span class="p1">(<span class="default"><a href="msafree.html#K13">FreeGen</a> <span class="p2">(<span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">F<sub>1</sub></font>() <a href="pre_circ.html#K2">--&gt;</a> <a href="numbers.html#K5">NAT</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="extens_1.html#T8">EXTENS_1:8</a></i>
;<br/>
<b>take </b>
<font color="Maroon">H</font>
;<br/>

<b>thus </b><a NAME="E10:5_1"/>
<font color="Maroon">H</font> <a href="msualg_3.html#R1">is_homomorphism</a> <font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()
 <b>by </b><i/>;<br/>

<b>thus </b><a NAME="E11:5_1"/>
<font color="Maroon">F<sub>5</sub></font>() <a href="birkhoff.html#K1" target="_self">-hash</a>  <a href="pboole.html#R6">=</a> <font color="Maroon">H</font> <a href="msualg_3.html#K3">**</a> <span class="p1">(<span class="default"><font color="Maroon">F<sub>4</sub></font>() <a href="birkhoff.html#K1" target="_self">-hash</a> </span>)</span>
 <b>by </b><i>, , , <a class="ref" href="extens_1.html#T18">EXTENS_1:18</a></i>;<br/>


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