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<b>let </b><font color="Maroon" title="c1">K</font>, <font color="Maroon" title="c2">L</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="robbins1.html#L3" title="ROBBINS1:struct.3">OrthoLattStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="robbins1.html#G3" title="ROBBINS1:aggr.3">OrthoLattStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">K</font>,the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c1">K</font>,the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <font color="Maroon" title="c1">K</font>,the <a href="robbins1.html#U1" title="ROBBINS1:sel.1">Compl</a> of <font color="Maroon" title="c1">K</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="robbins1.html#G3" title="ROBBINS1:aggr.3">OrthoLattStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">L</font>,the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c2">L</font>,the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <font color="Maroon" title="c2">L</font>,the <a href="robbins1.html#U1" title="ROBBINS1:sel.1">Compl</a> of <font color="Maroon" title="c2">L</font> #) &amp; <font color="Maroon" title="c1">K</font> is <a href="robbins3.html#V8" title="ROBBINS3:attr.8">involutive</a> implies <font color="Maroon" title="c2">L</font> is <a href="robbins3.html#V8" title="ROBBINS3:attr.8">involutive</a> )</span><br/>

<b>assume </b><a NAME="E1:49"/><i><font color="Green" title="E24">A1</font></i>: 
(  <a href="robbins1.html#G3" title="ROBBINS1:aggr.3">OrthoLattStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">K</font>,the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c1">K</font>,the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <font color="Maroon" title="c1">K</font>,the <a href="robbins1.html#U1" title="ROBBINS1:sel.1">Compl</a> of <font color="Maroon" title="c1">K</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="robbins1.html#G3" title="ROBBINS1:aggr.3">OrthoLattStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">L</font>,the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c2">L</font>,the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <font color="Maroon" title="c2">L</font>,the <a href="robbins1.html#U1" title="ROBBINS1:sel.1">Compl</a> of <font color="Maroon" title="c2">L</font> #) &amp; <font color="Maroon" title="c1">K</font> is <a href="robbins3.html#V8" title="ROBBINS3:attr.8">involutive</a> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">L</font> is <a href="robbins3.html#V8" title="ROBBINS3:attr.8">involutive</a></span><br/>

<a NAME="E2:49"/>
for <font color="Olive" title="b1">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">x</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="49_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c3">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x</font></span><br/>

<b>reconsider </b><font color="Maroon" title="c4">x'</font> = <font color="Maroon" title="c3">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">K</font> <b>by </b><i><a class="txt" href="robbins3.html#E1:49"><i><font color="Green" title="E24">A1</font></i></a></i>;<br/>
<a NAME="E2:49_1"/>
<font color="Maroon" title="c3">x</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x'</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> 
 
<b>by </b><i><a class="txt" href="robbins3.html#E1:49"><i><font color="Green" title="E24">A1</font></i></a>, <a class="ref" href="robbins3.html#T18" target="_self" title="ROBBINS3:th.18">Th18</a></i>;<br/>
<b>then </b><span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a>  = 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">x'</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> 
<b>by </b><i><a class="txt" href="robbins3.html#E1:49"><i><font color="Green" title="E24">A1</font></i></a>, <a class="ref" href="robbins3.html#T18" target="_self" title="ROBBINS3:th.18">Th18</a></i>
<br/>.= 
<font color="Maroon" title="c3">x</font>
<b>by </b><i><a class="txt" href="robbins3.html#E1:49"><i><font color="Green" title="E24">A1</font></i></a>, <a class="ref" href="robbins3.html#D6" target="_self" title="ROBBINS3:def.6">Def6</a></i>
;<br/>
<b>hence </b><a NAME="E4:49_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:49"/>
<font color="Maroon" title="c2">L</font> is <a href="robbins3.html#V8" title="ROBBINS3:attr.8">involutive</a>
 <b>by </b><i><a class="ref" href="robbins3.html#D6" target="_self" title="ROBBINS3:def.6">Def6</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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