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

<b>assume </b><a NAME="E1:45"/><i><font color="Green">E22</font></i>: 
(  <a href="lattices.html#G3">LattStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">K</font>,the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">K</font>,the <a href="lattices.html#U1">L_meet</a> of <font color="Maroon">K</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">L</font>,the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">L</font>,the <a href="lattices.html#U1">L_meet</a> of <font color="Maroon">L</font> #) &amp; <font color="Maroon">K</font> is <a href="lattices.html#V10">Lattice-like</a> )
 ;<br/>

<a NAME="E2:45"/><b>then </b>
( <font color="Maroon">K</font> is <a href="lattices.html#V4">join-commutative</a> &amp; <font color="Maroon">K</font> is <a href="lattices.html#V5">join-associative</a> &amp; <font color="Maroon">K</font> is <a href="lattices.html#V8">meet-absorbing</a> &amp; <font color="Maroon">K</font> is <a href="lattices.html#V6">meet-commutative</a> &amp; <font color="Maroon">K</font> is <a href="lattices.html#V7">meet-associative</a> &amp; <font color="Maroon">K</font> is <a href="lattices.html#V9">join-absorbing</a> )
 
<b>by </b><i><a class="ref" href="lattices.html#D10">LATTICES:def 10</a></i>;<br/>
<a NAME="E3:45"/><b>then </b>
( <font color="Maroon">L</font> is <a href="lattices.html#V4">join-commutative</a> &amp; <font color="Maroon">L</font> is <a href="lattices.html#V5">join-associative</a> &amp; <font color="Maroon">L</font> is <a href="lattices.html#V8">meet-absorbing</a> &amp; <font color="Maroon">L</font> is <a href="lattices.html#V6">meet-commutative</a> &amp; <font color="Maroon">L</font> is <a href="lattices.html#V7">meet-associative</a> &amp; <font color="Maroon">L</font> is <a href="lattices.html#V9">join-absorbing</a> )
 
<b>by </b><i><a class="ref" href="robbins3.html#D3" target="_self">Def3</a>, , <a class="ref" href="robbins3.html#D2" target="_self">Def2</a>, , , , <a class="ref" href="robbins3.html#D1" target="_self">Def1</a></i>;<br/>
<b>hence </b><a NAME="E4:45"/>
<font color="Maroon">L</font> is <a href="lattices.html#V10">Lattice-like</a>
 <b>by </b><i><a class="ref" href="lattices.html#D10">LATTICES:def 10</a></i>;<br/>


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