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<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">thus </span><a NAME="E1:69_1_1"/>
 for <font color="Olive" title="b1">u</font>, <font color="Olive" title="b2">v</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">u</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Olive" title="b2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">v</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Olive" title="b1">u</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>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="lattices.html#D4" onmouseover="rs('lattices/D4')" onmouseout="rh()">LATTICES:def 4</a>,<a class="ref" href="lattices.html#D10" onmouseover="rs('lattices/D10')" onmouseout="rh()">LATTICES:def 10</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"> (  <a href="normform.html#K11" title="NORMFORM:func.11">NormForm</a> <font color="Maroon" title="c1">A</font> is  <a href="lattices.html#V5" title="LATTICES:attr.5">join-associative</a>  &amp;  <a href="normform.html#K11" title="NORMFORM:func.11">NormForm</a> <font color="Maroon" title="c1">A</font> is  <a href="lattices.html#V8" title="LATTICES:attr.8">meet-absorbing</a>  &amp;  <a href="normform.html#K11" title="NORMFORM:func.11">NormForm</a> <font color="Maroon" title="c1">A</font> is  <a href="lattices.html#V6" title="LATTICES:attr.6">meet-commutative</a>  &amp;  <a href="normform.html#K11" title="NORMFORM:func.11">NormForm</a> <font color="Maroon" title="c1">A</font> is  <a href="lattices.html#V7" title="LATTICES:attr.7">meet-associative</a>  &amp;  <a href="normform.html#K11" title="NORMFORM:func.11">NormForm</a> <font color="Maroon" title="c1">A</font> is  <a href="lattices.html#V9" title="LATTICES:attr.9">join-absorbing</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E2:69_1_1"/>
 for <font color="Olive" title="b1">u</font>, <font color="Olive" title="b2">v</font>, <font color="Olive" title="b3">w</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">u</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">v</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Olive" title="b3">w</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">u</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Olive" title="b2">v</font></span>)</span> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Olive" title="b3">w</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="normform.html#E77"><span class="lab"><font color="Green" title="E49">Lm10</font></span></a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="lattices.html#D5" onmouseover="rs('lattices/D5')" onmouseout="rh()">LATTICES: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"> (  <a href="normform.html#K11" title="NORMFORM:func.11">NormForm</a> <font color="Maroon" title="c1">A</font> is  <a href="lattices.html#V8" title="LATTICES:attr.8">meet-absorbing</a>  &amp;  <a href="normform.html#K11" title="NORMFORM:func.11">NormForm</a> <font color="Maroon" title="c1">A</font> is  <a href="lattices.html#V6" title="LATTICES:attr.6">meet-commutative</a>  &amp;  <a href="normform.html#K11" title="NORMFORM:func.11">NormForm</a> <font color="Maroon" title="c1">A</font> is  <a href="lattices.html#V7" title="LATTICES:attr.7">meet-associative</a>  &amp;  <a href="normform.html#K11" title="NORMFORM:func.11">NormForm</a> <font color="Maroon" title="c1">A</font> is  <a href="lattices.html#V9" title="LATTICES:attr.9">join-absorbing</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E3:69_1_1"/>
 for <font color="Olive" title="b1">u</font>, <font color="Olive" title="b2">v</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  <span class="p1">(<span class="default"><font color="Olive" title="b1">u</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Olive" title="b2">v</font></span>)</span> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Olive" title="b2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">v</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>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="lattices.html#D8" onmouseover="rs('lattices/D8')" onmouseout="rh()">LATTICES:def 8</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"> (  <a href="normform.html#K11" title="NORMFORM:func.11">NormForm</a> <font color="Maroon" title="c1">A</font> is  <a href="lattices.html#V6" title="LATTICES:attr.6">meet-commutative</a>  &amp;  <a href="normform.html#K11" title="NORMFORM:func.11">NormForm</a> <font color="Maroon" title="c1">A</font> is  <a href="lattices.html#V7" title="LATTICES:attr.7">meet-associative</a>  &amp;  <a href="normform.html#K11" title="NORMFORM:func.11">NormForm</a> <font color="Maroon" title="c1">A</font> is  <a href="lattices.html#V9" title="LATTICES:attr.9">join-absorbing</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E4:69_1_1"/>
 for <font color="Olive" title="b1">u</font>, <font color="Olive" title="b2">v</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">u</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Olive" title="b2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">v</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Olive" title="b1">u</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>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="lattices.html#D6" onmouseover="rs('lattices/D6')" onmouseout="rh()">LATTICES:def 6</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"> (  <a href="normform.html#K11" title="NORMFORM:func.11">NormForm</a> <font color="Maroon" title="c1">A</font> is  <a href="lattices.html#V7" title="LATTICES:attr.7">meet-associative</a>  &amp;  <a href="normform.html#K11" title="NORMFORM:func.11">NormForm</a> <font color="Maroon" title="c1">A</font> is  <a href="lattices.html#V9" title="LATTICES:attr.9">join-absorbing</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E5:69_1_1"/>
 for <font color="Olive" title="b1">u</font>, <font color="Olive" title="b2">v</font>, <font color="Olive" title="b3">w</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">u</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">v</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Olive" title="b3">w</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">u</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Olive" title="b2">v</font></span>)</span> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Olive" title="b3">w</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="normform.html#E81"><span class="lab"><font color="Green" title="E53">Lm14</font></span></a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="lattices.html#D7" onmouseover="rs('lattices/D7')" onmouseout="rh()">LATTICES:def 7</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">  <a href="normform.html#K11" title="NORMFORM:func.11">NormForm</a> <font color="Maroon" title="c1">A</font> is  <a href="lattices.html#V9" title="LATTICES:attr.9">join-absorbing</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c3">u</font>, <font color="Maroon" title="c4">v</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>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="lattices.html#D9" onmouseover="rs('lattices/D9')" onmouseout="rh()">LATTICES:def 9</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"> <font color="Maroon" title="c3">u</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">u</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c4">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">u</font></span><br/>

<span class="kw">thus </span><a NAME="E6:69_1_1"/>
<font color="Maroon" title="c3">u</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">u</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Maroon" title="c4">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">u</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="normform.html#E83"><span class="lab"><font color="Green" title="E55">Lm16</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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