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<b>reconsider </b><font color="Maroon" title="c1">SN</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon">F<sub>1</sub></font>() <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  as  <a href="relat_1.html#V2" title="RELAT_1:attr.2">V5</a>  <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon">F<sub>1</sub></font>() ;<br/>
<b>let </b><font color="Maroon" title="c2">B</font> be  <a href="msualg_1.html#V5" title="MSUALG_1:attr.5">non-empty</a>  <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon">F<sub>1</sub></font>(); <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon" title="c2">B</font>] implies <font color="Maroon" title="c2">B</font> <a href="equation.html#R1" title="EQUATION:pred.1">|=</a> <font color="Maroon">F<sub>5</sub></font>() <a href="equation.html#K5" title="EQUATION:func.5">'='</a> <font color="Maroon">F<sub>6</sub></font>() )</span><br/>

<b>assume </b><a NAME="E2:6_1"/><i><font color="Green" title="E5">A3</font></i>: 
<font color="Maroon">P<sub>1</sub></font>[<font color="Maroon" title="c2">B</font>]
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">B</font> <a href="equation.html#R1" title="EQUATION:pred.1">|=</a> <font color="Maroon">F<sub>5</sub></font>() <a href="equation.html#K5" title="EQUATION:func.5">'='</a> <font color="Maroon">F<sub>6</sub></font>()</span><br/>

<b>let </b><font color="Maroon" title="c3">h</font> be   <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <span class="p1">(<span class="default"><a href="equation.html#K3" title="EQUATION:func.3">TermAlg</a> <font color="Maroon">F<sub>1</sub></font>()</span>)</span>,<font color="Maroon" title="c2">B</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="equation.html#D5" title="EQUATION:def.5">EQUATION:def 5</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c3">h</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a>  <a href="equation.html#K3" title="EQUATION:func.3">TermAlg</a> <font color="Maroon">F<sub>1</sub></font>(),<font color="Maroon" title="c2">B</font> or <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F<sub>5</sub></font>() <a href="equation.html#K5" title="EQUATION:func.5">'='</a> <font color="Maroon">F<sub>6</sub></font>()</span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F<sub>5</sub></font>() <a href="equation.html#K5" title="EQUATION:func.5">'='</a> <font color="Maroon">F<sub>6</sub></font>()</span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> </span>)</span> )</span><br/>

<b>assume </b><a NAME="E3:6_1"/><i><font color="Green" title="E6">A4</font></i>: 
<font color="Maroon" title="c3">h</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a>  <a href="equation.html#K3" title="EQUATION:func.3">TermAlg</a> <font color="Maroon">F<sub>1</sub></font>(),<font color="Maroon" title="c2">B</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F<sub>5</sub></font>() <a href="equation.html#K5" title="EQUATION:func.5">'='</a> <font color="Maroon">F<sub>6</sub></font>()</span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F<sub>5</sub></font>() <a href="equation.html#K5" title="EQUATION:func.5">'='</a> <font color="Maroon">F<sub>6</sub></font>()</span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> </span>)</span></span><br/>

<b>reconsider </b><font color="Maroon" title="c4">h1</font> = <font color="Maroon" title="c3">h</font> as   <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <span class="p1">(<span class="default"><a href="msafree.html#K11" title="MSAFREE:func.11">FreeMSA</a> <font color="Maroon" title="c1">SN</font></span>)</span>,<font color="Maroon" title="c2">B</font> ;<br/>
<b>set </b><font color="Maroon" title="c5">alfa</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c4">h1</font> <a href="msafree.html#K1" title="MSAFREE:func.1">||</a> <span class="p2">(<span class="default"><a href="msafree.html#K13" title="MSAFREE:func.13">FreeGen</a> <font color="Maroon" title="c1">SN</font></span>)</span></span>)</span> <a href="msualg_3.html#K3" title="MSUALG_3:func.3">**</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msafree.html#K15" title="MSAFREE:func.15">Reverse</a> <font color="Maroon" title="c1">SN</font></span>)</span> <a href="msualg_3.html#K4" title="MSUALG_3:func.4">""</a> </span>)</span>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">alfa1</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c4">h1</font> <a href="msafree.html#K1" title="MSAFREE:func.1">||</a> <span class="p2">(<span class="default"><a href="msafree.html#K13" title="MSAFREE:func.13">FreeGen</a> <font color="Maroon" title="c1">SN</font></span>)</span></span>)</span> <a href="msualg_3.html#K3" title="MSUALG_3:func.3">**</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msafree.html#K15" title="MSAFREE:func.15">Reverse</a> <font color="Maroon" title="c1">SN</font></span>)</span> <a href="msualg_3.html#K4" title="MSUALG_3:func.4">""</a> </span>)</span> as    <a href="pboole.html#M3" title="PBOOLE:mode.3">ManySortedFunction</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon">F<sub>1</sub></font>() <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c2">B</font> ;<br/>
<b>reconsider </b><font color="Maroon" title="c7">fi1</font> = <font color="Maroon">F<sub>3</sub></font>() as    <a href="pboole.html#M3" title="PBOOLE:mode.3">ManySortedFunction</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon">F<sub>1</sub></font>() <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon">F<sub>2</sub></font>() ;<br/>
<a NAME="E7:6_1"/><i><font color="Green" title="E7">A5</font></i>: 
<font color="Maroon">P<sub>1</sub></font>[<font color="Maroon" title="c2">B</font>]
 
<b>by </b><i><a class="txt" href="birkhoff.html#E2:6_1"><i><font color="Green" title="E5">A3</font></i></a></i>;<br/>
<a NAME="E8:6_1"/><i><font color="Green" title="E8">A6</font></i>: 
for <font color="Olive" title="b1">C</font> being <a href="msualg_1.html#V5" title="MSUALG_1:attr.5">non-empty</a>  <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon">F<sub>1</sub></font>()<br/> for <font color="Olive" title="b2">G</font> being   <a href="pboole.html#M3" title="PBOOLE:mode.3">ManySortedFunction</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon">F<sub>1</sub></font>() <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Olive" title="b1">C</font>  st <font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b1">C</font>] holds <br/> ex <font color="Olive" title="b3">h</font> being  <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <font color="Maroon">F<sub>2</sub></font>(),<font color="Olive" title="b1">C</font> st <br/>( <font color="Olive" title="b3">h</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a> <font color="Maroon">F<sub>2</sub></font>(),<font color="Olive" title="b1">C</font> &amp; <font color="Olive" title="b2">G</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Olive" title="b3">h</font> <a href="msualg_3.html#K3" title="MSUALG_3:func.3">**</a> <font color="Maroon" title="c7">fi1</font> )
 
<b>by </b><i><a class="txt" href="birkhoff.html#E2:6"><i><font color="Green" title="E4">A2</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon" title="c8">H</font> being   <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon" title="c2">B</font><b> such that </b><br/><a NAME="E10:6_1"/>
<font color="Maroon" title="c8">H</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a> <font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon" title="c2">B</font>
 <b>and </b><br/><a NAME="E11:6_1"/><i><font color="Green" title="E9">A7</font></i>: 
<font color="Maroon" title="c6">alfa1</font> <a href="birkhoff.html#K1" title="BIRKHOFF:func.1">-hash</a>  <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c8">H</font> <a href="msualg_3.html#K3" title="MSUALG_3:func.3">**</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">fi1</font> <a href="birkhoff.html#K1" title="BIRKHOFF:func.1">-hash</a> </span>)</span>
 <b>from </b><i><a class="ref" href="birkhoff.html#S3" target="_self" title="BIRKHOFF:sch.3">BIRKHOFF:sch 3</a>(<a class="txt" href="birkhoff.html#E7:6_1"><i><font color="Green" title="E7">A5</font></i></a>, <a class="txt" href="birkhoff.html#E8:6_1"><i><font color="Green" title="E8">A6</font></i></a>);<br/></i>
<a NAME="E12:6_1"/><i><font color="Green" title="E10">A8</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">h1</font> <a href="msafree.html#K1" title="MSAFREE:func.1">||</a> <span class="p3">(<span class="default"><a href="msafree.html#K13" title="MSAFREE:func.13">FreeGen</a> <font color="Maroon" title="c1">SN</font></span>)</span></span>)</span> <a href="msualg_3.html#K3" title="MSUALG_3:func.3">**</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="msafree.html#K15" title="MSAFREE:func.15">Reverse</a> <font color="Maroon" title="c1">SN</font></span>)</span> <a href="msualg_3.html#K4" title="MSUALG_3:func.4">""</a> </span>)</span></span>)</span> <a href="birkhoff.html#K1" title="BIRKHOFF:func.1">-hash</a>  <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a>  <a href="msafree.html#K11" title="MSAFREE:func.11">FreeMSA</a> <font color="Maroon" title="c1">SN</font>,<font color="Maroon" title="c2">B</font>
 
<b>by </b><i><a class="ref" href="birkhoff.html#D1" target="_self" title="BIRKHOFF:def.1">Def1</a></i>;<br/>
<a NAME="E13:6_1"/>
 <a href="mssubfam.html#K2" title="MSSUBFAM:func.2">rngs</a> <span class="p1">(<span class="default"><a href="msafree.html#K15" title="MSAFREE:func.15">Reverse</a> <font color="Maroon" title="c1">SN</font></span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c1">SN</font>
 
<b>by </b><i><a class="ref" href="extens_1.html#T14" title="EXTENS_1:th.14">EXTENS_1:14</a></i>;<br/>
<a NAME="E14:6_1"/><b>then </b><i><font color="Green" title="E11">A9</font></i>: 
(  <a href="msafree.html#K15" title="MSAFREE:func.15">Reverse</a> <font color="Maroon" title="c1">SN</font> is <a href="msualg_3.html#V1" title="MSUALG_3:attr.1">"1-1"</a> &amp;  <a href="msafree.html#K15" title="MSAFREE:func.15">Reverse</a> <font color="Maroon" title="c1">SN</font> is <a href="msualg_3.html#V2" title="MSUALG_3:attr.2">"onto"</a> )
 
<b>by </b><i><a class="ref" href="extens_1.html#T13" title="EXTENS_1:th.13">EXTENS_1:13</a>, <a class="ref" href="msualg_9.html#T12" title="MSUALG_9:th.12">MSUALG_9:12</a></i>;<br/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">h1</font> <a href="msafree.html#K1" title="MSAFREE:func.1">||</a> <span class="p4">(<span class="default"><a href="msafree.html#K13" title="MSAFREE:func.13">FreeGen</a> <font color="Maroon" title="c1">SN</font></span>)</span></span>)</span> <a href="msualg_3.html#K3" title="MSUALG_3:func.3">**</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="msafree.html#K15" title="MSAFREE:func.15">Reverse</a> <font color="Maroon" title="c1">SN</font></span>)</span> <a href="msualg_3.html#K4" title="MSUALG_3:func.4">""</a> </span>)</span></span>)</span> <a href="birkhoff.html#K1" title="BIRKHOFF:func.1">-hash</a> </span>)</span> <a href="msafree.html#K1" title="MSAFREE:func.1">||</a> <span class="p1">(<span class="default"><a href="msafree.html#K13" title="MSAFREE:func.13">FreeGen</a> <font color="Maroon" title="c1">SN</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">h1</font> <a href="msafree.html#K1" title="MSAFREE:func.1">||</a> <span class="p3">(<span class="default"><a href="msafree.html#K13" title="MSAFREE:func.13">FreeGen</a> <font color="Maroon" title="c1">SN</font></span>)</span></span>)</span> <a href="msualg_3.html#K3" title="MSUALG_3:func.3">**</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="msafree.html#K15" title="MSAFREE:func.15">Reverse</a> <font color="Maroon" title="c1">SN</font></span>)</span> <a href="msualg_3.html#K4" title="MSUALG_3:func.4">""</a> </span>)</span></span>)</span> <a href="msualg_3.html#K3" title="MSUALG_3:func.3">**</a> <span class="p1">(<span class="default"><a href="msafree.html#K15" title="MSAFREE:func.15">Reverse</a> <font color="Maroon" title="c1">SN</font></span>)</span>
<b>by </b><i><a class="ref" href="birkhoff.html#D1" target="_self" title="BIRKHOFF:def.1">Def1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">h1</font> <a href="msafree.html#K1" title="MSAFREE:func.1">||</a> <span class="p2">(<span class="default"><a href="msafree.html#K13" title="MSAFREE:func.13">FreeGen</a> <font color="Maroon" title="c1">SN</font></span>)</span></span>)</span> <a href="msualg_3.html#K3" title="MSUALG_3:func.3">**</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="msafree.html#K15" title="MSAFREE:func.15">Reverse</a> <font color="Maroon" title="c1">SN</font></span>)</span> <a href="msualg_3.html#K4" title="MSUALG_3:func.4">""</a> </span>)</span> <a href="msualg_3.html#K3" title="MSUALG_3:func.3">**</a> <span class="p2">(<span class="default"><a href="msafree.html#K15" title="MSAFREE:func.15">Reverse</a> <font color="Maroon" title="c1">SN</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="autalg_1.html#T13" title="AUTALG_1:th.13">AUTALG_1:13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">h1</font> <a href="msafree.html#K1" title="MSAFREE:func.1">||</a> <span class="p2">(<span class="default"><a href="msafree.html#K13" title="MSAFREE:func.13">FreeGen</a> <font color="Maroon" title="c1">SN</font></span>)</span></span>)</span> <a href="msualg_3.html#K3" title="MSUALG_3:func.3">**</a> <span class="p1">(<span class="default"><a href="msualg_3.html#K2" title="MSUALG_3:func.2">id</a> <span class="p2">(<span class="default"><a href="msafree.html#K13" title="MSAFREE:func.13">FreeGen</a> <font color="Maroon" title="c1">SN</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="birkhoff.html#E14:6_1"><i><font color="Green" title="E11">A9</font></i></a>, <a class="ref" href="msualg_3.html#T5" title="MSUALG_3:th.5">MSUALG_3:5</a></i>
<br/>.= 
<font color="Maroon" title="c4">h1</font> <a href="msafree.html#K1" title="MSAFREE:func.1">||</a> <span class="p1">(<span class="default"><a href="msafree.html#K13" title="MSAFREE:func.13">FreeGen</a> <font color="Maroon" title="c1">SN</font></span>)</span>
<b>by </b><i><a class="ref" href="msualg_3.html#T3" title="MSUALG_3:th.3">MSUALG_3:3</a></i>
;<br/>
<a NAME="E16:6_1"/><b>then </b><i><font color="Green" title="E12">A10</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">h1</font> <a href="msafree.html#K1" title="MSAFREE:func.1">||</a> <span class="p3">(<span class="default"><a href="msafree.html#K13" title="MSAFREE:func.13">FreeGen</a> <font color="Maroon" title="c1">SN</font></span>)</span></span>)</span> <a href="msualg_3.html#K3" title="MSUALG_3:func.3">**</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="msafree.html#K15" title="MSAFREE:func.15">Reverse</a> <font color="Maroon" title="c1">SN</font></span>)</span> <a href="msualg_3.html#K4" title="MSUALG_3:func.4">""</a> </span>)</span></span>)</span> <a href="birkhoff.html#K1" title="BIRKHOFF:func.1">-hash</a>  <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c4">h1</font>
 
<b>by </b><i><a class="txt" href="birkhoff.html#E3:6_1"><i><font color="Green" title="E6">A4</font></i></a>, <a class="txt" href="birkhoff.html#E12:6_1"><i><font color="Green" title="E10">A8</font></i></a>, <a class="ref" href="extens_1.html#T18" title="EXTENS_1:th.18">EXTENS_1:18</a></i>;<br/>
<i><font color="Green" title="E13">A11</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">h1</font> <a href="msafree.html#K1" title="MSAFREE:func.1">||</a> <span class="p5">(<span class="default"><a href="msafree.html#K13" title="MSAFREE:func.13">FreeGen</a> <font color="Maroon" title="c1">SN</font></span>)</span></span>)</span> <a href="msualg_3.html#K3" title="MSUALG_3:func.3">**</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="msafree.html#K15" title="MSAFREE:func.15">Reverse</a> <font color="Maroon" title="c1">SN</font></span>)</span> <a href="msualg_3.html#K4" title="MSUALG_3:func.4">""</a> </span>)</span></span>)</span> <a href="birkhoff.html#K1" title="BIRKHOFF:func.1">-hash</a> </span>)</span> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon">F<sub>5</sub></font>() = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">H</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">F<sub>3</sub></font>() <a href="birkhoff.html#K1" title="BIRKHOFF:func.1">-hash</a> </span>)</span> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon">F<sub>5</sub></font>()
<b>by </b><i><a class="txt" href="birkhoff.html#E11:6_1"><i><font color="Green" title="E9">A7</font></i></a>, <a class="ref" href="msualg_3.html#T2" title="MSUALG_3:th.2">MSUALG_3:2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">H</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">F<sub>3</sub></font>() <a href="birkhoff.html#K1" title="BIRKHOFF:func.1">-hash</a> </span>)</span> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon">F<sub>6</sub></font>()</span>)</span>
<b>by </b><i><a class="txt" href="birkhoff.html#E1:6"><i><font color="Green" title="E3">A1</font></i></a>, <a class="ref" href="funct_2.html#T21" title="FUNCT_2:th.21">FUNCT_2:21</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">H</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">F<sub>3</sub></font>() <a href="birkhoff.html#K1" title="BIRKHOFF:func.1">-hash</a> </span>)</span> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon">F<sub>6</sub></font>()
<b>by </b><i><a class="ref" href="funct_2.html#T21" title="FUNCT_2:th.21">FUNCT_2:21</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">h1</font> <a href="msafree.html#K1" title="MSAFREE:func.1">||</a> <span class="p5">(<span class="default"><a href="msafree.html#K13" title="MSAFREE:func.13">FreeGen</a> <font color="Maroon" title="c1">SN</font></span>)</span></span>)</span> <a href="msualg_3.html#K3" title="MSUALG_3:func.3">**</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="msafree.html#K15" title="MSAFREE:func.15">Reverse</a> <font color="Maroon" title="c1">SN</font></span>)</span> <a href="msualg_3.html#K4" title="MSUALG_3:func.4">""</a> </span>)</span></span>)</span> <a href="birkhoff.html#K1" title="BIRKHOFF:func.1">-hash</a> </span>)</span> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon">F<sub>6</sub></font>()
<b>by </b><i><a class="txt" href="birkhoff.html#E11:6_1"><i><font color="Green" title="E9">A7</font></i></a>, <a class="ref" href="msualg_3.html#T2" title="MSUALG_3:th.2">MSUALG_3:2</a></i>
;<br/>
<b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>()</span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon">F<sub>5</sub></font>()
<b>by </b><i><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>()</span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> </span>)</span>
<b>by </b><i><a class="txt" href="birkhoff.html#E16:6_1"><i><font color="Green" title="E12">A10</font></i></a>, <a class="txt" href="birkhoff.html#E17:6_1"><i><font color="Green" title="E13">A11</font></i></a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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