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<span class="kw">let </span><font color="Maroon" title="c1">L</font> be   <a href="nelson_1.html#NM3" title="NELSON_1:NM.3">Nelson_Algebra</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">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds  <span class="p1">(<span class="default"><a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="nelson_1.html#K1" title="NELSON_1:func.1">=&gt;</a> <font color="Olive" title="b1">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">b</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</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"><a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="nelson_1.html#K1" title="NELSON_1:func.1">=&gt;</a> <font color="Maroon" title="c2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">b</font></span><br/>



<a NAME="E1:65"/>
<font color="Maroon" title="c2">b</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="nelson_1.html#R1" title="NELSON_1:pred.1">&lt;</a> <font color="Maroon" title="c2">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nelson_1.html#D7" target="_self" onmouseover="rs('nelson_1/D7')" onmouseout="rh()">Def2</a></span>;<br/>
<a NAME="E2:65"/><span class="kw">then </span><span class="lab"><font color="Green" title="E47">A1</font></span>: 
<font color="Maroon" title="c2">b</font> <a href="nelson_1.html#R1" title="NELSON_1:pred.1">&lt;</a> <span class="p1">(<span class="default"><a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="nelson_1.html#K1" title="NELSON_1:func.1">=&gt;</a> <font color="Maroon" title="c2">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nelson_1.html#D10" target="_self" onmouseover="rs('nelson_1/D10')" onmouseout="rh()">Def4</a></span>;<br/>
<a NAME="E3:65"/>
 <a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="nelson_1.html#K1" title="NELSON_1:func.1">=&gt;</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="nelson_1.html#R1" title="NELSON_1:pred.1">&lt;</a> <span class="p1">(<span class="default"><a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">b</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nelson_1.html#D16" target="_self" onmouseover="rs('nelson_1/D16')" onmouseout="rh()">Def10</a></span>;<br/>
<a NAME="E4:65"/><span class="kw">then </span><span class="lab"><font color="Green" title="E48">A2</font></span>: 
<font color="Maroon" title="c2">b</font> <a href="nelson_1.html#R2" title="NELSON_1:pred.2">&lt;=</a> <span class="p1">(<span class="default"><a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="nelson_1.html#K1" title="NELSON_1:func.1">=&gt;</a> <font color="Maroon" title="c2">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:65"><span class="lab"><font color="Green" title="E47">A1</font></span></a>, <a class="ref" href="nelson_1.html#T9" target="_self" onmouseover="rs('nelson_1/T9')" onmouseout="rh()">Th5</a></span>;<br/>
<a NAME="E5:65"/><span class="lab"><font color="Green" title="E49">A3</font></span>: 
<span class="p1">(<span class="default"><a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="nelson_1.html#K1" title="NELSON_1:func.1">=&gt;</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="nelson_1.html#R1" title="NELSON_1:pred.1">&lt;</a> <font color="Maroon" title="c2">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nelson_1.html#T33" target="_self" onmouseover="rs('nelson_1/T33')" onmouseout="rh()">Th17</a></span>;<br/>
<a NAME="E6:65"/>
<span class="p1">(<span class="default"><a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="nelson_1.html#R1" title="NELSON_1:pred.1">&lt;</a>  <a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="nelson_1.html#K1" title="NELSON_1:func.1">=&gt;</a> <font color="Maroon" title="c2">b</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nelson_1.html#D15" target="_self" onmouseover="rs('nelson_1/D15')" onmouseout="rh()">Def9</a></span>;<br/>
<a NAME="E7:65"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="nelson_1.html#K1" title="NELSON_1:func.1">=&gt;</a> <font color="Maroon" title="c2">b</font> <a href="nelson_1.html#R2" title="NELSON_1:pred.2">&lt;=</a> <font color="Maroon" title="c2">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nelson_1.html#T9" target="_self" onmouseover="rs('nelson_1/T9')" onmouseout="rh()">Th5</a>, <a class="txt" href="#E5:65"><span class="lab"><font color="Green" title="E49">A3</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:65"/>
<span class="p1">(<span class="default"><a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="nelson_1.html#K1" title="NELSON_1:func.1">=&gt;</a> <font color="Maroon" title="c2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:65"><span class="lab"><font color="Green" title="E48">A2</font></span></a>, <a class="ref" href="nelson_1.html#T7" target="_self" onmouseover="rs('nelson_1/T7')" onmouseout="rh()">Th3</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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