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<span class="kw">reconsider </span><font color="Maroon" title="c1">fi1</font> = <font color="Maroon">F<sub>3</sub></font>() as    <a href="pboole.html#M2" title="PBOOLE:mode.2">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="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>, the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon">F<sub>2</sub></font>() ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c2">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="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> as  <a href="relat_1.html#V2" title="RELAT_1:attr.2">V2</a>() <a href="pboole.html#NM1" title="PBOOLE:NM.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/>
<span class="kw">let </span><font color="Maroon" title="c3">B</font> be   <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a>   <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> over <font color="Maroon">F<sub>1</sub></font>(); <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon" title="c3">B</font>] implies <font color="Maroon" title="c3">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/>

<span class="kw">assume </span><a NAME="E3:6_1"/>
<font color="Maroon">P<sub>1</sub></font>[<font color="Maroon" title="c3">B</font>]
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">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/>

<a NAME="E4:6_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E5">A3</font></span>: 
<font color="Maroon">P<sub>1</sub></font>[<font color="Maroon" title="c3">B</font>]
 
;<br/>
<span class="kw">let </span><font color="Maroon" title="c4">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="c3">B</font>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="equation.html#D5" onmouseover="rs('equation/D5')" onmouseout="rh()">EQUATION:def 5</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c4">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="c3">B</font> or <span class="p1">(<span class="default"><font color="Maroon" title="c4">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="xtuple_0.html#K1" title="XTUPLE_0: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="c4">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="xtuple_0.html#K2" title="XTUPLE_0:func.2">`2</a></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E5:6_1"/><span class="lab"><font color="Green" title="E6">A4</font></span>: 
<font color="Maroon" title="c4">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="c3">B</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c4">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="xtuple_0.html#K1" title="XTUPLE_0: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="c4">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="xtuple_0.html#K2" title="XTUPLE_0:func.2">`2</a></span>)</span></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c5">h1</font> = <font color="Maroon" title="c4">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="c2">SN</font></span>)</span>,<font color="Maroon" title="c3">B</font> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">alfa</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c5">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="c2">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="c2">SN</font></span>)</span> <a href="msualg_3.html#K4" title="MSUALG_3:func.4">""</a></span>)</span>;<br/>
<a NAME="E7:6_1"/><span class="lab"><font color="Green" title="E7">A5</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">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="c2">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="c2">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="c2">SN</font>,<font color="Maroon" title="c3">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="birkhoff.html#D1" target="_self" onmouseover="rs('birkhoff/D1')" onmouseout="rh()">Def1</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c7">alfa1</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c5">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="c2">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="c2">SN</font></span>)</span> <a href="msualg_3.html#K4" title="MSUALG_3:func.4">""</a></span>)</span> as    <a href="pboole.html#M2" title="PBOOLE:mode.2">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="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>, the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c3">B</font> ;<br/>
<a NAME="E9:6_1"/><span class="lab"><font color="Green" title="E8">A6</font></span>: 
 for <font color="Olive" title="b1">C</font> being   <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a>   <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> over <font color="Maroon">F<sub>1</sub></font>()<br/>  for <font color="Olive" title="b2">G</font> being    <a href="pboole.html#M2" title="PBOOLE:mode.2">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="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>, the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">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#R8" title="PBOOLE:pred.8">=</a> <font color="Olive" title="b3">h</font> <a href="msualg_3.html#K3" title="MSUALG_3:func.3">**</a> <font color="Maroon" title="c1">fi1</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:6"><span class="lab"><font color="Green" title="E4">A2</font></span></a></span>;<br/>
<span class="kw">consider </span><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="c3">B</font><span class="kw"> such that </span><br/><a NAME="E11:6_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="c3">B</font>
 <span class="kw">and </span><br/><a NAME="E12:6_1"/><span class="lab"><font color="Green" title="E9">A7</font></span>: 
<font color="Maroon" title="c7">alfa1</font> <a href="birkhoff.html#K1" title="BIRKHOFF:func.1">-hash</a>  <a href="pboole.html#R8" title="PBOOLE:pred.8">=</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="c1">fi1</font> <a href="birkhoff.html#K1" title="BIRKHOFF:func.1">-hash</a></span>)</span>
 <span class="kw">from</span> <span class="lab"><a class="ref" href="birkhoff.html#S3" target="_self" onmouseover="rs('birkhoff/S3')" onmouseout="rh()">BIRKHOFF:sch 3</a>(<a class="txt" href="#E4:6_1"><span class="lab"><font color="Green" title="E5">A3</font></span></a>, <a class="txt" href="#E9:6_1"><span class="lab"><font color="Green" title="E8">A6</font></span></a>);<br/></span>
<span class="lab"><font color="Green" title="E10">A8</font></span>: <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="c5">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="c2">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="c2">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>()
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:6_1"><span class="lab"><font color="Green" title="E9">A7</font></span></a>, <a class="ref" href="msualg_3.html#T2" onmouseover="rs('msualg_3/T2')" onmouseout="rh()">MSUALG_3:2</a></span>
<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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:6"><span class="lab"><font color="Green" title="E3">A1</font></span></a>, <a class="ref" href="funct_2.html#T15" onmouseover="rs('funct_2/T15')" onmouseout="rh()">FUNCT_2:15</a></span>
<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>()
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T15" onmouseover="rs('funct_2/T15')" onmouseout="rh()">FUNCT_2:15</a></span>
<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="c5">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="c2">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="c2">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>()
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:6_1"><span class="lab"><font color="Green" title="E9">A7</font></span></a>, <a class="ref" href="msualg_3.html#T2" onmouseover="rs('msualg_3/T2')" onmouseout="rh()">MSUALG_3:2</a></span>
;<br/>
<a NAME="E14:6_1"/>
 <a href="funct_6.html#K2" title="FUNCT_6: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="c2">SN</font></span>)</span> <a href="pboole.html#R8" title="PBOOLE:pred.8">=</a> <font color="Maroon" title="c2">SN</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="extens_1.html#T10" onmouseover="rs('extens_1/T10')" onmouseout="rh()">EXTENS_1:10</a></span>;<br/>
<a NAME="E15:6_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E11">A9</font></span>: 
(  <a href="msafree.html#K15" title="MSAFREE:func.15">Reverse</a> <font color="Maroon" title="c2">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="c2">SN</font> is  <a href="msualg_3.html#V2" title="MSUALG_3:attr.2">"onto"</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="extens_1.html#T9" onmouseover="rs('extens_1/T9')" onmouseout="rh()">EXTENS_1:9</a>, <a class="ref" href="msualg_9.html#T11" onmouseover="rs('msualg_9/T11')" onmouseout="rh()">MSUALG_9:11</a></span>;<br/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">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="c2">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="c2">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="c2">SN</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">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="c2">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="c2">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="c2">SN</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="birkhoff.html#D1" target="_self" onmouseover="rs('birkhoff/D1')" onmouseout="rh()">Def1</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">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="c2">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="c2">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="c2">SN</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#T140" onmouseover="rs('pboole/T140')" onmouseout="rh()">PBOOLE:140</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">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="c2">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="c2">SN</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:6_1"><span class="lab"><font color="Green" title="E11">A9</font></span></a>, <a class="ref" href="msualg_3.html#T5" onmouseover="rs('msualg_3/T5')" onmouseout="rh()">MSUALG_3:5</a></span>
<br/>.= 
<font color="Maroon" title="c5">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="c2">SN</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_3.html#T3" onmouseover="rs('msualg_3/T3')" onmouseout="rh()">MSUALG_3:3</a></span>
;<br/>
<a NAME="E17:6_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E12">A10</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">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="c2">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="c2">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#R8" title="PBOOLE:pred.8">=</a> <font color="Maroon" title="c5">h1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:6_1"><span class="lab"><font color="Green" title="E6">A4</font></span></a>, <a class="txt" href="#E7:6_1"><span class="lab"><font color="Green" title="E7">A5</font></span></a>, <a class="ref" href="extens_1.html#T14" onmouseover="rs('extens_1/T14')" onmouseout="rh()">EXTENS_1:14</a></span>;<br/>
<span class="kw">thus </span><span class="p1">(<span class="default"><font color="Maroon" title="c4">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="xtuple_0.html#K1" title="XTUPLE_0:func.1">`1</a></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">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>()

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">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="xtuple_0.html#K2" title="XTUPLE_0:func.2">`2</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:6_1"><span class="lab"><font color="Green" title="E12">A10</font></span></a>, <a class="txt" href="#E13:6_1"><span class="lab"><font color="Green" title="E10">A8</font></span></a></span>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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