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<span class="kw">let </span><font color="Maroon" title="c1">L</font> be   <a href="robbins3.html#NM1" title="ROBBINS3:NM.1">Ortholattice</a>; <a class="txt" 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>, <font color="Olive" title="b3">c</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>  st <font color="Olive" title="b1">a</font> <a href="robbins4.html#NR2" title="ROBBINS4:NR.2">_|_</a> <font color="Olive" title="b2">b</font> &amp; <font color="Olive" title="b1">a</font> <a href="robbins4.html#NR2" title="ROBBINS4:NR.2">_|_</a> <font color="Olive" title="b3">c</font> holds <br/>( <font color="Olive" title="b1">a</font> <a href="robbins4.html#NR2" title="ROBBINS4:NR.2">_|_</a> <font color="Olive" title="b2">b</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Olive" title="b3">c</font> &amp; <font color="Olive" title="b1">a</font> <a href="robbins4.html#NR2" title="ROBBINS4:NR.2">_|_</a> <font color="Olive" title="b2">b</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b3">c</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font>, <font color="Maroon" title="c4">c</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" 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="robbins4.html#NR2" title="ROBBINS4:NR.2">_|_</a> <font color="Maroon" title="c3">b</font> &amp; <font color="Maroon" title="c2">a</font> <a href="robbins4.html#NR2" title="ROBBINS4:NR.2">_|_</a> <font color="Maroon" title="c4">c</font> implies ( <font color="Maroon" title="c2">a</font> <a href="robbins4.html#NR2" title="ROBBINS4:NR.2">_|_</a> <font color="Maroon" title="c3">b</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c2">a</font> <a href="robbins4.html#NR2" title="ROBBINS4:NR.2">_|_</a> <font color="Maroon" title="c3">b</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c4">c</font> ) )</span><br/>







<span class="kw">assume </span><a NAME="E1:50"/>
<font color="Maroon" title="c2">a</font> <a href="robbins4.html#NR2" title="ROBBINS4:NR.2">_|_</a> <font color="Maroon" title="c3">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c2">a</font> <a href="robbins4.html#NR2" title="ROBBINS4:NR.2">_|_</a> <font color="Maroon" title="c4">c</font> or ( <font color="Maroon" title="c2">a</font> <a href="robbins4.html#NR2" title="ROBBINS4:NR.2">_|_</a> <font color="Maroon" title="c3">b</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c2">a</font> <a href="robbins4.html#NR2" title="ROBBINS4:NR.2">_|_</a> <font color="Maroon" title="c3">b</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c4">c</font> ) )</span><br/>

<a NAME="E2:50"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A1</font></span>: 
<font color="Maroon" title="c2">a</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c3">b</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="robbins4.html#D5" target="_self" title="ROBBINS4:def.5">Def5</a></span>;<br/>
<a NAME="E3:50"/><span class="kw">then </span><span class="lab"><font color="Green" title="E36">A2</font></span>: 
<font color="Maroon" title="c2">a</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#T9" title="LATTICES:th.9">LATTICES:9</a></span>;<br/>
<span class="kw">assume </span><a NAME="E4:50"/><span class="lab"><font color="Green" title="E37">A3</font></span>: 
<font color="Maroon" title="c2">a</font> <a href="robbins4.html#NR2" title="ROBBINS4:NR.2">_|_</a> <font color="Maroon" title="c4">c</font>
 ; <a class="txt" 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="robbins4.html#NR2" title="ROBBINS4:NR.2">_|_</a> <font color="Maroon" title="c3">b</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c2">a</font> <a href="robbins4.html#NR2" title="ROBBINS4:NR.2">_|_</a> <font color="Maroon" title="c3">b</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c4">c</font> )</span><br/>

<a NAME="E5:50"/>
<font color="Maroon" title="c3">b</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a>  <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#T5" title="LATTICES:th.5">LATTICES:5</a></span>;<br/>
<a NAME="E6:50"/><span class="kw">then </span>
<font color="Maroon" title="c2">a</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:50"><span class="lab"><font color="Green" title="E35">A1</font></span></a>, <a class="ref" href="lattices.html#T7" title="LATTICES:th.7">LATTICES:7</a></span>;<br/>
<a NAME="E7:50"/><span class="kw">then </span>
<font color="Maroon" title="c2">a</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="robbins3.html#D6" title="ROBBINS3:def.6">ROBBINS3:def 6</a></span>;<br/>
<a NAME="E8:50"/><span class="kw">then </span>
<font color="Maroon" title="c2">a</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="robbins1.html#D23" title="ROBBINS1:def.23">ROBBINS1:def 23</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:50"/>
<font color="Maroon" title="c2">a</font> <a href="robbins4.html#NR2" title="ROBBINS4:NR.2">_|_</a> <font color="Maroon" title="c3">b</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c4">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="robbins4.html#D5" target="_self" title="ROBBINS4:def.5">Def5</a></span>; <a class="txt" 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="robbins4.html#NR2" title="ROBBINS4:NR.2">_|_</a> <font color="Maroon" title="c3">b</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c4">c</font></span><br/>

<a NAME="E10:50"/>
<font color="Maroon" title="c2">a</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c4">c</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:50"><span class="lab"><font color="Green" title="E37">A3</font></span></a>, <a class="ref" href="robbins4.html#D5" target="_self" title="ROBBINS4:def.5">Def5</a></span>;<br/>
<a NAME="E11:50"/><span class="kw">then </span>
<font color="Maroon" title="c2">a</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:50"><span class="lab"><font color="Green" title="E36">A2</font></span></a>, <a class="ref" href="lattices.html#T4" title="LATTICES:th.4">LATTICES:4</a></span>;<br/>
<a NAME="E12:50"/><span class="kw">then </span>
<font color="Maroon" title="c2">a</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="robbins1.html#D23" title="ROBBINS1:def.23">ROBBINS1:def 23</a></span>;<br/>
<a NAME="E13:50"/><span class="kw">then </span>
<font color="Maroon" title="c2">a</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</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"><span class="p3">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="robbins3.html#D6" title="ROBBINS3:def.6">ROBBINS3:def 6</a></span>;<br/>
<a NAME="E14:50"/><span class="kw">then </span>
<font color="Maroon" title="c2">a</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="robbins3.html#D6" title="ROBBINS3:def.6">ROBBINS3:def 6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E15:50"/>
<font color="Maroon" title="c2">a</font> <a href="robbins4.html#NR2" title="ROBBINS4:NR.2">_|_</a> <font color="Maroon" title="c3">b</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c4">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="robbins4.html#D5" target="_self" title="ROBBINS4:def.5">Def5</a></span>; <a class="txt" 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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