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<span class="kw">let </span><font color="Maroon" title="c1">K</font>, <font color="Maroon" title="c2">L</font> be  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="lattices.html#L3" title="LATTICES:struct.3">LattStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">K</font>,the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c1">K</font>,the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <font color="Maroon" title="c1">K</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">L</font>,the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c2">L</font>,the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <font color="Maroon" title="c2">L</font> #) &amp; <font color="Maroon" title="c1">K</font> is  <a href="lattices.html#V10" title="LATTICES:attr.10">Lattice-like</a>  implies <font color="Maroon" title="c2">L</font> is  <a href="lattices.html#V10" title="LATTICES:attr.10">Lattice-like</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:45"/>
(  <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">K</font>,the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c1">K</font>,the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <font color="Maroon" title="c1">K</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">L</font>,the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c2">L</font>,the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <font color="Maroon" title="c2">L</font> #) &amp; <font color="Maroon" title="c1">K</font> is  <a href="lattices.html#V10" title="LATTICES:attr.10">Lattice-like</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">L</font> is  <a href="lattices.html#V10" title="LATTICES:attr.10">Lattice-like</a> </span><br/>

<a NAME="E2:45"/><span class="kw">then </span>
( <font color="Maroon" title="c2">L</font> is  <a href="lattices.html#V4" title="LATTICES:attr.4">join-commutative</a>  &amp; <font color="Maroon" title="c2">L</font> is  <a href="lattices.html#V5" title="LATTICES:attr.5">join-associative</a>  &amp; <font color="Maroon" title="c2">L</font> is  <a href="lattices.html#V8" title="LATTICES:attr.8">meet-absorbing</a>  &amp; <font color="Maroon" title="c2">L</font> is  <a href="lattices.html#V6" title="LATTICES:attr.6">meet-commutative</a>  &amp; <font color="Maroon" title="c2">L</font> is  <a href="lattices.html#V7" title="LATTICES:attr.7">meet-associative</a>  &amp; <font color="Maroon" title="c2">L</font> is  <a href="lattices.html#V9" title="LATTICES:attr.9">join-absorbing</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="robbins3.html#T9" target="_self" title="ROBBINS3:th.9">Th9</a>, <a class="ref" href="robbins3.html#T10" target="_self" title="ROBBINS3:th.10">Th10</a>, <a class="ref" href="robbins3.html#T11" target="_self" title="ROBBINS3:th.11">Th11</a>, <a class="ref" href="robbins3.html#T12" target="_self" title="ROBBINS3:th.12">Th12</a>, <a class="ref" href="robbins3.html#T13" target="_self" title="ROBBINS3:th.13">Th13</a>, <a class="ref" href="robbins3.html#T14" target="_self" title="ROBBINS3:th.14">Th14</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:45"/>
<font color="Maroon" title="c2">L</font> is  <a href="lattices.html#V10" title="LATTICES:attr.10">Lattice-like</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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