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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">a</font>, <font color="Olive" title="b2">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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> holds  <font color="Olive" title="b1">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Olive" title="b2">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font></span><br/>

<span class="kw">set </span><font color="Maroon" title="c2">G</font> =  <a href="normform.html#K11" title="NORMFORM:func.11">NormForm</a> <font color="Maroon" title="c1">A</font>;<br/>
<span class="kw">let </span><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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 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">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c5">a9</font> = <font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c6">b9</font> = <font color="Maroon" title="c4">b</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="ref" href="normform.html#D12" target="_self" onmouseover="rs('normform/D12')" onmouseout="rh()">Def12</a></span>;<br/>
<span class="kw">thus </span><font color="Maroon" title="c3">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c4">b</font></span>)</span> = 
 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="c5">a9</font>,<font color="Maroon" title="c5">a9</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="c5">a9</font>,<font color="Maroon" title="c6">b9</font>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="normform.html#E82"><span class="lab"><font color="Green" title="E54">Lm15</font></span></a></span>
<br/>.= 
 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"><a href="normform.html#K9" title="NORMFORM:func.9">mi</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">a9</font> <a href="normform.html#K10" title="NORMFORM:func.10">^</a> <font color="Maroon" title="c5">a9</font></span>)</span></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="c5">a9</font>,<font color="Maroon" title="c6">b9</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/>.= 
 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"><a href="normform.html#K9" title="NORMFORM:func.9">mi</a> <font color="Maroon" title="c5">a9</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="c5">a9</font>,<font color="Maroon" title="c6">b9</font>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="normform.html#T55" target="_self" onmouseover="rs('normform/T55')" onmouseout="rh()">Th55</a></span>
<br/>.= 
<font color="Maroon" title="c3">a</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c4">b</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="normform.html#T42" target="_self" onmouseover="rs('normform/T42')" onmouseout="rh()">Th42</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c3">a</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="normform.html#E76"><span class="lab"><font color="Green" title="E48">Lm9</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c3">a</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="normform.html#E80"><span class="lab"><font color="Green" title="E52">Lm13</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c3">a</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="normform.html#E79"><span class="lab"><font color="Green" title="E51">Lm12</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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