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<b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be  <a href="lattices.html#V3">strict</a>  <a href="lattices.html#L3">LattStr</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:1_1_2"/><i><font color="Green">E1</font></i>: 
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">c<sub>1</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> holds <br/>( <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">c<sub>2</sub></font>) <a href="binop_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Olive">b<sub>2</sub></font> &amp; <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">c<sub>2</sub></font>) <a href="binop_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="subset_1.html#K9">/\</a> <font color="Olive">b<sub>2</sub></font> ) ) )
 <b>and </b><br/><a NAME="E2:1_1_2"/><i><font color="Green">E2</font></i>: 
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">c<sub>1</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> holds <br/>( <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">c<sub>3</sub></font>) <a href="binop_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Olive">b<sub>2</sub></font> &amp; <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">c<sub>3</sub></font>) <a href="binop_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="subset_1.html#K9">/\</a> <font color="Olive">b<sub>2</sub></font> ) ) )
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">c<sub>2</sub></font>), <font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">c<sub>3</sub></font>), <font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">c<sub>2</sub></font>), <font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">c<sub>3</sub></font>) as   <a href="binop_1.html#NM2">BinOp</a> of  <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="txt" href="lattice3.html#E1:1_1_2"><i><font color="Green">E1</font></i></a>, <a class="txt" href="lattice3.html#E2:1_1_2"><i><font color="Green">E2</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">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font> be   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>thus </b><font color="Maroon">c<sub>4</sub></font> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font> = 
<font color="Maroon">c<sub>8</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="txt" href="lattice3.html#E1:1_1_2"><i><font color="Green">E1</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>5</sub></font> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="txt" href="lattice3.html#E2:1_1_2"><i><font color="Green">E2</font></i></a></i>
;<br/></div><b>end;</b></div>
<a NAME="E5:1_1_2"/><b>then </b><i><font color="Green">E3</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="binop_1.html#T2">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">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font> be   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>thus </b><font color="Maroon">c<sub>6</sub></font> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font> = 
<font color="Maroon">c<sub>8</sub></font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="txt" href="lattice3.html#E1:1_1_2"><i><font color="Green">E1</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>7</sub></font> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="txt" href="lattice3.html#E2:1_1_2"><i><font color="Green">E2</font></i></a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E7:1_1_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="lattice3.html#E1:1_1_2"><i><font color="Green">E1</font></i></a>, <a class="txt" href="lattice3.html#E2:1_1_2"><i><font color="Green">E2</font></i></a>, <a class="txt" href="lattice3.html#E5:1_1_2"><i><font color="Green">E3</font></i></a>, <a class="ref" href="binop_1.html#T2">BINOP_1:2</a></i>;<br/>


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