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<b>let </b><font color="Maroon">L1</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="lattices.html#L3">LattStr</a> , <font color="Maroon">L2</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="lattices.html#L3">LattStr</a> ;<br/>

<b>assume </b><a NAME="E1:7"/><i><font color="Green">E14</font></i>: 
 <a href="lattices.html#G3">LattStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L1</font>,the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">L1</font>,the <a href="lattices.html#U1">L_meet</a> of <font color="Maroon">L1</font> #) <a href="hidden.html#R1">=</a>  <a href="lattices.html#G3">LattStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L2</font>,the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">L2</font>,the <a href="lattices.html#U1">L_meet</a> of <font color="Maroon">L2</font> #)
 ;<br/>

<b>let </b><font color="Maroon">a1</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L1</font>, <font color="Maroon">b1</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L1</font>;<br/><b>let </b><font color="Maroon">a2</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L2</font>, <font color="Maroon">b2</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L2</font>;<br/>



<b>assume </b><a NAME="E2:7"/><i><font color="Green">E15</font></i>: 
( <font color="Maroon">a1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a2</font> &amp; <font color="Maroon">b1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b2</font> )
 ;<br/>

<b>thus </b><a NAME="E3:7"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">a1</font> <a href="lattices.html#K1">"\/"</a> <font color="Maroon">b1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a2</font> <a href="lattices.html#K1">"\/"</a> <font color="Maroon">b2</font>
 <b>by </b><i>, </i>;<br/>

<b>thus </b><a NAME="E4:7"/>
<font color="Maroon">a1</font> <a href="lattices.html#K2">"/\"</a> <font color="Maroon">b1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a2</font> <a href="lattices.html#K2">"/\"</a> <font color="Maroon">b2</font>
 <b>by </b><i>, </i>;<br/>

<a NAME="E5:7"/>
( ( <font color="Maroon">a1</font> <a href="lattices.html#R1">[=</a> <font color="Maroon">b1</font> implies <font color="Maroon">a1</font> <a href="lattices.html#K1">"\/"</a> <font color="Maroon">b1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b1</font> ) &amp; ( <font color="Maroon">a1</font> <a href="lattices.html#K1">"\/"</a> <font color="Maroon">b1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b1</font> implies <font color="Maroon">a1</font> <a href="lattices.html#R1">[=</a> <font color="Maroon">b1</font> ) &amp; ( <font color="Maroon">a2</font> <a href="lattices.html#K1">"\/"</a> <font color="Maroon">b2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b2</font> implies <font color="Maroon">a2</font> <a href="lattices.html#R1">[=</a> <font color="Maroon">b2</font> ) &amp; ( <font color="Maroon">a2</font> <a href="lattices.html#R1">[=</a> <font color="Maroon">b2</font> implies <font color="Maroon">a2</font> <a href="lattices.html#K1">"\/"</a> <font color="Maroon">b2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b2</font> ) )
 
<b>by </b><i><a class="ref" href="lattices.html#D3">LATTICES:def 3</a></i>;<br/>
<b>hence </b><a NAME="E6:7"/>
( <font color="Maroon">a1</font> <a href="lattices.html#R1">[=</a> <font color="Maroon">b1</font> iff <font color="Maroon">a2</font> <a href="lattices.html#R1">[=</a> <font color="Maroon">b2</font> )
 <b>by </b><i>, </i>;<br/>


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