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<b>let </b><font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c2">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="robbins4.html#K1" title="ROBBINS4:func.1">B_6</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="robbins4.html#K2" title="ROBBINS4:func.2">Benzene</a>   st <font color="Maroon" title="c1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x</font> &amp; <font color="Maroon" title="c2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> holds <br/>( <font color="Maroon" title="c1">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c2">b</font> iff <font color="Olive" title="b1">x</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Olive" title="b2">y</font> )</span><br/><b>let </b><font color="Maroon" title="c3">x</font>, <font color="Maroon" title="c4">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="robbins4.html#K2" title="ROBBINS4:func.2">Benzene</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">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x</font> &amp; <font color="Maroon" title="c2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">y</font> implies ( <font color="Maroon" title="c1">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c2">b</font> iff <font color="Maroon" title="c3">x</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c4">y</font> ) )</span><br/>



<b>assume </b><a NAME="E1:27"/><i><font color="Green" title="E20">A0</font></i>: 
( <font color="Maroon" title="c1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x</font> &amp; <font color="Maroon" title="c2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">y</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c2">b</font> iff <font color="Maroon" title="c3">x</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c4">y</font> )</span><br/>

<div><b>hereby </b> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">x</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c4">y</font> implies <font color="Maroon" title="c1">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c2">b</font> )</span>
<div class="add"><b>assume </b><a NAME="E1:27_1"/>
<font color="Maroon" title="c1">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c2">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">x</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c4">y</font></span><br/><a NAME="E2:27_1"/><b>then </b>
<font color="Maroon" title="c3">x</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a>  <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c4">y</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a> 
 <b>by </b><i><a class="ref" href="robbins4.html#T1" target="_self" title="ROBBINS4:th.1">Strict</a>, <a class="txt" href="#E1:27"><i><font color="Green" title="E20">A0</font></i></a>, <a class="ref" href="robbins4.html#T12" target="_self" title="ROBBINS4:th.12">Strict2</a></i>;<br/><b>hence </b><a NAME="E3:27_1"/>
<font color="Maroon" title="c3">x</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c4">y</font>
 <b>by </b><i><a class="ref" href="lattice3.html#T7" title="LATTICE3:th.7">LATTICE3:7</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>assume </b><a NAME="E3:27"/>
<font color="Maroon" title="c3">x</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c4">y</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c2">b</font></span><br/>

<a NAME="E4:27"/><b>then </b>
<font color="Maroon" title="c3">x</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a>  <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c4">y</font> <a href="lattice3.html#K4" title="LATTICE3:func.4">%</a> 
 
<b>by </b><i><a class="ref" href="lattice3.html#T7" title="LATTICE3:th.7">LATTICE3:7</a></i>;<br/>
<b>hence </b><a NAME="E5:27"/>
<font color="Maroon" title="c1">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c2">b</font>
 <b>by </b><i><a class="txt" href="#E1:27"><i><font color="Green" title="E20">A0</font></i></a>, <a class="ref" href="robbins4.html#T12" target="_self" title="ROBBINS4:th.12">Strict2</a>, <a class="ref" href="robbins4.html#T1" target="_self" title="ROBBINS4:th.1">Strict</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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