<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">A1</font>, <font color="Maroon" title="c2">A2</font> be  <a href="robbins1.html#V3" title="ROBBINS1:attr.3">strict</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="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A1</font>,the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c1">A1</font>,the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <font color="Maroon" title="c1">A1</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattice3.html#K14" title="LATTICE3:func.14">latt</a> <a href="robbins4.html#K1" title="ROBBINS4:func.1">B_6</a>  &amp; ( for <font color="Olive" title="b1">x</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A1</font><br/> for <font color="Olive" title="b2">y</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of 3  st <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> holds <br/>the <a href="robbins1.html#U1" title="ROBBINS1:sel.1">Compl</a> of <font color="Maroon" title="c1">A1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  ) &amp;  <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">A2</font>,the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c2">A2</font>,the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <font color="Maroon" title="c2">A2</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattice3.html#K14" title="LATTICE3:func.14">latt</a> <a href="robbins4.html#K1" title="ROBBINS4:func.1">B_6</a>  &amp; ( for <font color="Olive" title="b1">x</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">A2</font><br/> for <font color="Olive" title="b2">y</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of 3  st <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> holds <br/>the <a href="robbins1.html#U1" title="ROBBINS1:sel.1">Compl</a> of <font color="Maroon" title="c2">A2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  ) implies <font color="Maroon" title="c1">A1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">A2</font> )</span><br/>

<b>assume </b><b>that </b><br/><a NAME="E1:22_1_2"/><i><font color="Green" title="E14">A0</font></i>: 
(  <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A1</font>,the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c1">A1</font>,the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <font color="Maroon" title="c1">A1</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattice3.html#K14" title="LATTICE3:func.14">latt</a> <a href="robbins4.html#K1" title="ROBBINS4:func.1">B_6</a>  &amp; ( for <font color="Olive" title="b1">x</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A1</font><br/> for <font color="Olive" title="b2">y</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of 3  st <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> holds <br/>the <a href="robbins1.html#U1" title="ROBBINS1:sel.1">Compl</a> of <font color="Maroon" title="c1">A1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  ) )
 <b>and </b><br/><a NAME="E2:22_1_2"/><i><font color="Green" title="E15">A2</font></i>: 
(  <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">A2</font>,the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c2">A2</font>,the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <font color="Maroon" title="c2">A2</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattice3.html#K14" title="LATTICE3:func.14">latt</a> <a href="robbins4.html#K1" title="ROBBINS4:func.1">B_6</a>  &amp; ( for <font color="Olive" title="b1">x</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">A2</font><br/> for <font color="Olive" title="b2">y</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of 3  st <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> holds <br/>the <a href="robbins1.html#U1" title="ROBBINS1:sel.1">Compl</a> of <font color="Maroon" title="c2">A2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  ) )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">A1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">A2</font></span><br/>

<b>set </b><font color="Maroon" title="c3">M</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A1</font>;<br/>
<b>set </b><font color="Maroon" title="c4">f1</font> = the <a href="robbins1.html#U1" title="ROBBINS1:sel.1">Compl</a> of <font color="Maroon" title="c1">A1</font>;<br/>
<b>set </b><font color="Maroon" title="c5">f2</font> = the <a href="robbins1.html#U1" title="ROBBINS1:sel.1">Compl</a> of <font color="Maroon" title="c2">A2</font>;<br/>
<a NAME="E3:22_1_2"/>
for <font color="Olive" title="b1">x</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A1</font> holds  the <a href="robbins1.html#U1" title="ROBBINS1:sel.1">Compl</a> of <font color="Maroon" title="c1">A1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="robbins1.html#U1" title="ROBBINS1:sel.1">Compl</a> of <font color="Maroon" title="c2">A2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c6">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> the <a href="robbins1.html#U1" title="ROBBINS1:sel.1">Compl</a> of <font color="Maroon" title="c1">A1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="robbins1.html#U1" title="ROBBINS1:sel.1">Compl</a> of <font color="Maroon" title="c2">A2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font></span><br/>

<b>reconsider </b><font color="Maroon" title="c7">y</font> = <font color="Maroon" title="c6">x</font> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of 3 <b>by </b><i><a class="txt" href="#E1:22_1_2"><i><font color="Green" title="E14">A0</font></i></a>, <a class="ref" href="robbins4.html#T8" target="_self" title="ROBBINS4:th.8">CosikX1</a></i>;<br/>
<b>thus </b>the <a href="robbins1.html#U1" title="ROBBINS1:sel.1">Compl</a> of <font color="Maroon" title="c1">A1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> = 
<font color="Maroon" title="c7">y</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
<b>by </b><i><a class="txt" href="#E1:22_1_2"><i><font color="Green" title="E14">A0</font></i></a></i>
<br/>.= 
the <a href="robbins1.html#U1" title="ROBBINS1:sel.1">Compl</a> of <font color="Maroon" title="c2">A2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font>
<b>by </b><i><a class="txt" href="#E2:22_1_2"><i><font color="Green" title="E15">A2</font></i></a>, <a class="txt" href="#E1:22_1_2"><i><font color="Green" title="E14">A0</font></i></a></i>
; <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="E4:22_1_2"/>
<font color="Maroon" title="c1">A1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">A2</font>
 <b>by </b><i><a class="txt" href="#E1:22_1_2"><i><font color="Green" title="E14">A0</font></i></a>, <a class="txt" href="#E2:22_1_2"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="funct_2.html#T113" title="FUNCT_2:th.113">FUNCT_2:113</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
