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<b>let </b><font color="Maroon" title="c2">L1</font>, <font color="Maroon" title="c3">L2</font> be  <a href="lattices.html#V3" title="LATTICES:attr.3">strict</a>  <a href="lattices.html#L3" title="LATTICES:struct.3">LattStr</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:1_1_2"/><i><font color="Green" title="E1">A3</font></i>: 
( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">L1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <font color="Maroon" title="c1">X</font> &amp; ( for <font color="Olive" title="b1">Y</font>, <font color="Olive" title="b2">Z</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> holds <br/> ( <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c2">L1</font>) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b1">Y</font>,<font color="Olive" title="b2">Z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">Y</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Olive" title="b2">Z</font> &amp; <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon" title="c2">L1</font>) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b1">Y</font>,<font color="Olive" title="b2">Z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">Y</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Olive" title="b2">Z</font> ) ) )
 <b>and </b><br/><a NAME="E2:1_1_2"/><i><font color="Green" title="E2">A4</font></i>: 
( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">L2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <font color="Maroon" title="c1">X</font> &amp; ( for <font color="Olive" title="b1">Y</font>, <font color="Olive" title="b2">Z</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> holds <br/> ( <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c3">L2</font>) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b1">Y</font>,<font color="Olive" title="b2">Z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">Y</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Olive" title="b2">Z</font> &amp; <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon" title="c3">L2</font>) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b1">Y</font>,<font color="Olive" title="b2">Z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">Y</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Olive" title="b2">Z</font> ) ) )
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c4">j1</font> = <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c2">L1</font>), <font color="Maroon" title="c5">j2</font> = <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c3">L2</font>), <font color="Maroon" title="c6">m1</font> = <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon" title="c2">L1</font>), <font color="Maroon" title="c7">m2</font> = <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon" title="c3">L2</font>) as   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="txt" href="lattice3.html#E1:1_1_2"><i><font color="Green" title="E1">A3</font></i></a>, <a class="txt" href="lattice3.html#E2:1_1_2"><i><font color="Green" title="E2">A4</font></i></a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="1_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c8">x</font>, <font color="Maroon" title="c9">y</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>;<br/><b>thus </b><font color="Maroon" title="c4">j1</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c9">y</font> = 
<font color="Maroon" title="c8">x</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c9">y</font>
<b>by </b><i><a class="txt" href="lattice3.html#E1:1_1_2"><i><font color="Green" title="E1">A3</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c5">j2</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c9">y</font>
<b>by </b><i><a class="txt" href="lattice3.html#E2:1_1_2"><i><font color="Green" title="E2">A4</font></i></a></i>
;<br/></div><b>end;</b></div>
<a NAME="E5:1_1_2"/><b>then </b><i><font color="Green" title="E3">A5</font></i>: 
<font color="Maroon" title="c4">j1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c5">j2</font>
 
<b>by </b><i><a class="ref" href="binop_1.html#T2" title="BINOP_1:th.2">BINOP_1:2</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="1_1_2_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c8">x</font>, <font color="Maroon" title="c9">y</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>;<br/><b>thus </b><font color="Maroon" title="c6">m1</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c9">y</font> = 
<font color="Maroon" title="c8">x</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c9">y</font>
<b>by </b><i><a class="txt" href="lattice3.html#E1:1_1_2"><i><font color="Green" title="E1">A3</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c7">m2</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c9">y</font>
<b>by </b><i><a class="txt" href="lattice3.html#E2:1_1_2"><i><font color="Green" title="E2">A4</font></i></a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E7:1_1_2"/>
<font color="Maroon" title="c2">L1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">L2</font>
 <b>by </b><i><a class="txt" href="lattice3.html#E1:1_1_2"><i><font color="Green" title="E1">A3</font></i></a>, <a class="txt" href="lattice3.html#E2:1_1_2"><i><font color="Green" title="E2">A4</font></i></a>, <a class="txt" href="lattice3.html#E5:1_1_2"><i><font color="Green" title="E3">A5</font></i></a>, <a class="ref" href="binop_1.html#T2" title="BINOP_1:th.2">BINOP_1:2</a></i>;<br/>


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