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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">a</font>, <font color="Olive" title="b2">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  <font color="Olive" title="b1">a</font> <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="Olive" title="b1">a</font></span>)</span> <a href="nelson_1.html#R2" title="NELSON_1:pred.2">&lt;=</a> <font color="Olive" title="b2">b</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Olive" title="b2">b</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">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"> <font color="Maroon" title="c2">a</font> <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">a</font></span>)</span> <a href="nelson_1.html#R2" title="NELSON_1:pred.2">&lt;=</a> <font color="Maroon" title="c3">b</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c3">b</font></span>)</span></span><br/>





 <a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c3">b</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c3">b</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> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c3">b</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="nelson_1.html#T1" target="_self" onmouseover="rs('nelson_1/T1')" onmouseout="rh()">Th1</a></span>
<br/>.= 
<font color="Maroon" title="c3">b</font> <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="c3">b</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="robbins3.html#D6" onmouseover="rs('robbins3/D6')" onmouseout="rh()">ROBBINS3:def 6</a></span>
;<br/>
<a NAME="E2:57"/><span class="kw">then </span>
 <a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c3">b</font></span>)</span></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"><font color="Maroon" title="c2">a</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p2">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c2">a</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nelson_1.html#D19" target="_self" onmouseover="rs('nelson_1/D19')" onmouseout="rh()">Def13</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:57"/>
<font color="Maroon" title="c2">a</font> <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">a</font></span>)</span> <a href="nelson_1.html#R2" title="NELSON_1:pred.2">&lt;=</a> <font color="Maroon" title="c3">b</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><a href="robbins1.html#NK11" title="ROBBINS1:NK.11">-</a> <font color="Maroon" title="c3">b</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nelson_1.html#D19" target="_self" onmouseover="rs('nelson_1/D19')" onmouseout="rh()">Def13</a>, <a class="ref" href="nelson_1.html#T9" target="_self" onmouseover="rs('nelson_1/T9')" onmouseout="rh()">Th5</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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