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<span class="kw">set </span><font color="Maroon" title="c1">L</font> =  the  1 <a href="struct_0.html#V13" title="STRUCT_0:attr.13">-element</a>  <a href="robbins3.html#NM1" title="ROBBINS3:NM.1">Ortholattice</a>;<br/>
<a NAME="E1:9_1_1"/>
 the  1 <a href="struct_0.html#V13" title="STRUCT_0:attr.13">-element</a>  <a href="robbins3.html#NM1" title="ROBBINS3:NM.1">Ortholattice</a> is  <a href="robbins4.html#V1" title="ROBBINS4:attr.1">orthomodular</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="9_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of  the  1 <a href="struct_0.html#V13" title="STRUCT_0:attr.13">-element</a>  <a href="robbins3.html#NM1" title="ROBBINS3:NM.1">Ortholattice</a>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="robbins4.html#D1" target="_self" title="ROBBINS4:def.1">ROBBINS4:def 1</a> <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">x</font> <a href="lattices.html#R1" title="LATTICES:pred.1">[=</a> <font color="Maroon" title="c3">y</font> implies <font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c3">y</font></span>)</span> )</span><br/>

<span class="kw">thus </span><a NAME="E1:9_1_1_1"/>
( <font color="Maroon" title="c2">x</font> <a href="lattices.html#R1" title="LATTICES:pred.1">[=</a> <font color="Maroon" title="c3">y</font> implies <font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a></span>)</span> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c3">y</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="struct_0.html#D10" title="STRUCT_0:def.10">STRUCT_0:def 10</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/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E2:9_1_1"/>
 ex <font color="Olive">b<sub>1</sub></font> being   <a href="robbins3.html#NM1" title="ROBBINS3:NM.1">Ortholattice</a> st <br/>( <font color="Olive">b<sub>1</sub></font> is  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>  &amp; <font color="Olive">b<sub>1</sub></font> is  <a href="robbins4.html#V1" title="ROBBINS4:attr.1">orthomodular</a>  &amp; <font color="Olive">b<sub>1</sub></font> is  <a href="lattices.html#V12" title="LATTICES:attr.12">modular</a>  &amp; <font color="Olive">b<sub>1</sub></font> is  <a href="lattices.html#V17" title="LATTICES:attr.17">Boolean</a>  )
 ; <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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