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<span class="kw">let </span><font color="Maroon" title="c1">A</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</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">  for <font color="Olive" title="b1">K</font>, <font color="Olive" title="b2">L</font>, <font color="Olive" title="b3">M</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="normform.html#K8" title="NORMFORM:func.8">Normal_forms_on</a> <font color="Maroon" title="c1">A</font> holds   the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <span class="p1">(<span class="default"><a href="normform.html#K11" title="NORMFORM:func.11">NormForm</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b1">K</font>,<span class="p1">(<span class="default"> the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <span class="p2">(<span class="default"><a href="normform.html#K11" title="NORMFORM:func.11">NormForm</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b2">L</font>,<font color="Olive" title="b3">M</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <span class="p1">(<span class="default"><a href="normform.html#K11" title="NORMFORM:func.11">NormForm</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"> the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <span class="p2">(<span class="default"><a href="normform.html#K11" title="NORMFORM:func.11">NormForm</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b1">K</font>,<font color="Olive" title="b2">L</font>)</span>)</span>,<span class="p1">(<span class="default"> the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <span class="p2">(<span class="default"><a href="normform.html#K11" title="NORMFORM:func.11">NormForm</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b1">K</font>,<font color="Olive" title="b3">M</font>)</span>)</span>)</span><br/><span class="kw">let </span><font color="Maroon" title="c2">K</font>, <font color="Maroon" title="c3">L</font>, <font color="Maroon" title="c4">M</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="normform.html#K8" title="NORMFORM:func.8">Normal_forms_on</a> <font color="Maroon" title="c1">A</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">  the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <span class="p1">(<span class="default"><a href="normform.html#K11" title="NORMFORM:func.11">NormForm</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c2">K</font>,<span class="p1">(<span class="default"> the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <span class="p2">(<span class="default"><a href="normform.html#K11" title="NORMFORM:func.11">NormForm</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c3">L</font>,<font color="Maroon" title="c4">M</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <span class="p1">(<span class="default"><a href="normform.html#K11" title="NORMFORM:func.11">NormForm</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"> the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <span class="p2">(<span class="default"><a href="normform.html#K11" title="NORMFORM:func.11">NormForm</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c3">L</font>)</span>)</span>,<span class="p1">(<span class="default"> the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <span class="p2">(<span class="default"><a href="normform.html#K11" title="NORMFORM:func.11">NormForm</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c4">M</font>)</span>)</span>)</span><br/>







<a NAME="E1:67"/><span class="lab"><font color="Green" title="E55">A1</font></span>: 
 the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <span class="p1">(<span class="default"><a href="normform.html#K11" title="NORMFORM:func.11">NormForm</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c4">M</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="normform.html#K9" title="NORMFORM:func.9">mi</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">K</font> <a href="normform.html#K10" title="NORMFORM:func.10">^</a> <font color="Maroon" title="c4">M</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="normform.html#D12" target="_self" onmouseover="rs('normform/D12')" onmouseout="rh()">Def12</a></span>;<br/>
<a NAME="E2:67"/>
(  the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <span class="p1">(<span class="default"><a href="normform.html#K11" title="NORMFORM:func.11">NormForm</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c3">L</font>,<font color="Maroon" title="c4">M</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="normform.html#K9" title="NORMFORM:func.9">mi</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">L</font> <a href="setwiseo.html#K5" title="SETWISEO:func.5">\/</a> <font color="Maroon" title="c4">M</font></span>)</span> &amp;  the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <span class="p1">(<span class="default"><a href="normform.html#K11" title="NORMFORM:func.11">NormForm</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c3">L</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="normform.html#K9" title="NORMFORM:func.9">mi</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">K</font> <a href="normform.html#K10" title="NORMFORM:func.10">^</a> <font color="Maroon" title="c3">L</font></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="normform.html#D12" target="_self" onmouseover="rs('normform/D12')" onmouseout="rh()">Def12</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c5">La</font> =  the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <span class="p1">(<span class="default"><a href="normform.html#K11" title="NORMFORM:func.11">NormForm</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c3">L</font>,<font color="Maroon" title="c4">M</font>), <font color="Maroon" title="c6">Lb</font> =  the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <span class="p1">(<span class="default"><a href="normform.html#K11" title="NORMFORM:func.11">NormForm</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c3">L</font>), <font color="Maroon" title="c7">Lc</font> =  the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <span class="p1">(<span class="default"><a href="normform.html#K11" title="NORMFORM:func.11">NormForm</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c4">M</font>) as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="normform.html#K8" title="NORMFORM:func.8">Normal_forms_on</a> <font color="Maroon" title="c1">A</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:67"><span class="lab"><font color="Green" title="E55">A1</font></span></a></span>;<br/>
 the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <span class="p1">(<span class="default"><a href="normform.html#K11" title="NORMFORM:func.11">NormForm</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c2">K</font>,<span class="p1">(<span class="default"> the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <span class="p2">(<span class="default"><a href="normform.html#K11" title="NORMFORM:func.11">NormForm</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c3">L</font>,<font color="Maroon" title="c4">M</font>)</span>)</span>) = 
 <a href="normform.html#K9" title="NORMFORM:func.9">mi</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">K</font> <a href="normform.html#K10" title="NORMFORM:func.10">^</a> <font color="Maroon" title="c5">La</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="normform.html#D12" target="_self" onmouseover="rs('normform/D12')" onmouseout="rh()">Def12</a></span>
<br/>.= 
 <a href="normform.html#K9" title="NORMFORM:func.9">mi</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">K</font> <a href="normform.html#K10" title="NORMFORM:func.10">^</a> <span class="p2">(<span class="default"><a href="normform.html#K9" title="NORMFORM:func.9">mi</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">L</font> <a href="setwiseo.html#K5" title="SETWISEO:func.5">\/</a> <font color="Maroon" title="c4">M</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="normform.html#D12" target="_self" onmouseover="rs('normform/D12')" onmouseout="rh()">Def12</a></span>
<br/>.= 
 <a href="normform.html#K9" title="NORMFORM:func.9">mi</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">K</font> <a href="normform.html#K10" title="NORMFORM:func.10">^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">L</font> <a href="setwiseo.html#K5" title="SETWISEO:func.5">\/</a> <font color="Maroon" title="c4">M</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="normform.html#T51" target="_self" onmouseover="rs('normform/T51')" onmouseout="rh()">Th51</a></span>
<br/>.= 
 <a href="normform.html#K9" title="NORMFORM:func.9">mi</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">K</font> <a href="normform.html#K10" title="NORMFORM:func.10">^</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="setwiseo.html#K5" title="SETWISEO:func.5">\/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">K</font> <a href="normform.html#K10" title="NORMFORM:func.10">^</a> <font color="Maroon" title="c4">M</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="normform.html#T53" target="_self" onmouseover="rs('normform/T53')" onmouseout="rh()">Th53</a></span>
<br/>.= 
 <a href="normform.html#K9" title="NORMFORM:func.9">mi</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="normform.html#K9" title="NORMFORM:func.9">mi</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">K</font> <a href="normform.html#K10" title="NORMFORM:func.10">^</a> <font color="Maroon" title="c3">L</font></span>)</span></span>)</span> <a href="setwiseo.html#K5" title="SETWISEO:func.5">\/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">K</font> <a href="normform.html#K10" title="NORMFORM:func.10">^</a> <font color="Maroon" title="c4">M</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="normform.html#T44" target="_self" onmouseover="rs('normform/T44')" onmouseout="rh()">Th44</a></span>
<br/>.= 
 <a href="normform.html#K9" title="NORMFORM:func.9">mi</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="normform.html#K9" title="NORMFORM:func.9">mi</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">K</font> <a href="normform.html#K10" title="NORMFORM:func.10">^</a> <font color="Maroon" title="c3">L</font></span>)</span></span>)</span> <a href="setwiseo.html#K5" title="SETWISEO:func.5">\/</a> <span class="p2">(<span class="default"><a href="normform.html#K9" title="NORMFORM:func.9">mi</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">K</font> <a href="normform.html#K10" title="NORMFORM:func.10">^</a> <font color="Maroon" title="c4">M</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="normform.html#T44" target="_self" onmouseover="rs('normform/T44')" onmouseout="rh()">Th44</a></span>
<br/>.= 
 <a href="normform.html#K9" title="NORMFORM:func.9">mi</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">Lb</font> <a href="setwiseo.html#K5" title="SETWISEO:func.5">\/</a> <span class="p2">(<span class="default"><a href="normform.html#K9" title="NORMFORM:func.9">mi</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">K</font> <a href="normform.html#K10" title="NORMFORM:func.10">^</a> <font color="Maroon" title="c4">M</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="normform.html#D12" target="_self" onmouseover="rs('normform/D12')" onmouseout="rh()">Def12</a></span>
<br/>.= 
 <a href="normform.html#K9" title="NORMFORM:func.9">mi</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">Lb</font> <a href="setwiseo.html#K5" title="SETWISEO:func.5">\/</a> <font color="Maroon" title="c7">Lc</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="normform.html#D12" target="_self" onmouseover="rs('normform/D12')" onmouseout="rh()">Def12</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E5:67"/>
 the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <span class="p1">(<span class="default"><a href="normform.html#K11" title="NORMFORM:func.11">NormForm</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c2">K</font>,<span class="p1">(<span class="default"> the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <span class="p2">(<span class="default"><a href="normform.html#K11" title="NORMFORM:func.11">NormForm</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c3">L</font>,<font color="Maroon" title="c4">M</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <span class="p1">(<span class="default"><a href="normform.html#K11" title="NORMFORM:func.11">NormForm</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"> the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <span class="p2">(<span class="default"><a href="normform.html#K11" title="NORMFORM:func.11">NormForm</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c3">L</font>)</span>)</span>,<span class="p1">(<span class="default"> the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <span class="p2">(<span class="default"><a href="normform.html#K11" title="NORMFORM:func.11">NormForm</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c4">M</font>)</span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="normform.html#D12" target="_self" onmouseover="rs('normform/D12')" onmouseout="rh()">Def12</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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