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<span class="kw">let </span><font color="Maroon" title="c1">DL</font> be   <a href="lattices.html#V11" title="LATTICES:attr.11">distributive</a>   <a href="lattices.html#V14" title="LATTICES:attr.14">upper-bounded</a>  <a href="lattices.html#NM1" title="LATTICES:NM.1">Lattice</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">B</font> being   <a href="finsub_1.html#NM1" title="FINSUB_1:NM.1">Finite_Subset</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">DL</font><br/>  for <font color="Olive" title="b2">p</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">DL</font> holds  <span class="p1">(<span class="default"><a href="lattice4.html#K2" title="LATTICE4:func.2">FinMeet</a> <font color="Olive" title="b1">B</font></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattice4.html#K2" title="LATTICE4:func.2">FinMeet</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"> the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c1">DL</font> <a href="funcop_1.html#K9" title="FUNCOP_1:func.9">[:]</a> (<span class="p3">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c1">DL</font></span>)</span>,<font color="Olive" title="b2">p</font>)</span>)</span> <a href="setwiseo.html#K8" title="SETWISEO:func.8">.:</a> <font color="Olive" title="b1">B</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">B</font> be   <a href="finsub_1.html#NM1" title="FINSUB_1:NM.1">Finite_Subset</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">DL</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">p</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">DL</font> holds  <span class="p1">(<span class="default"><a href="lattice4.html#K2" title="LATTICE4:func.2">FinMeet</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattice4.html#K2" title="LATTICE4:func.2">FinMeet</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"> the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c1">DL</font> <a href="funcop_1.html#K9" title="FUNCOP_1:func.9">[:]</a> (<span class="p3">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c1">DL</font></span>)</span>,<font color="Olive" title="b1">p</font>)</span>)</span> <a href="setwiseo.html#K8" title="SETWISEO:func.8">.:</a> <font color="Maroon" title="c2">B</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">p</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">DL</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="lattice4.html#K2" title="LATTICE4:func.2">FinMeet</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattice4.html#K2" title="LATTICE4:func.2">FinMeet</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"> the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c1">DL</font> <a href="funcop_1.html#K9" title="FUNCOP_1:func.9">[:]</a> (<span class="p3">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c1">DL</font></span>)</span>,<font color="Maroon" title="c3">p</font>)</span>)</span> <a href="setwiseo.html#K8" title="SETWISEO:func.8">.:</a> <font color="Maroon" title="c2">B</font></span>)</span></span><br/>





<span class="kw">set </span><font color="Maroon" title="c4">J</font> =  the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c1">DL</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">M</font> =  the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <font color="Maroon" title="c1">DL</font>;<br/>
<span class="kw">thus </span><span class="p1">(<span class="default"><a href="lattice4.html#K2" title="LATTICE4:func.2">FinMeet</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">p</font> = 
 the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c1">DL</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<span class="p1">(<span class="default"> the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <font color="Maroon" title="c1">DL</font> <a href="setwiseo.html#K7" title="SETWISEO:func.7">$$</a> (<font color="Maroon" title="c2">B</font>,<span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c1">DL</font></span>)</span>)</span>)</span>,<font color="Maroon" title="c3">p</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattice2.html#D4" title="LATTICE2:def.4">LATTICE2:def 4</a></span>
<br/>.= 
 the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <font color="Maroon" title="c1">DL</font> <a href="setwiseo.html#K7" title="SETWISEO:func.7">$$</a> (<font color="Maroon" title="c2">B</font>,<span class="p1">(<span class="default"> the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c1">DL</font> <a href="funcop_1.html#K9" title="FUNCOP_1:func.9">[:]</a> (<span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c1">DL</font></span>)</span>,<font color="Maroon" title="c3">p</font>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="lattice4.html#E35"><span class="lab"><font color="Green" title="E25">Lm3</font></span></a></span>
<br/>.= 
 <a href="lattice2.html#K3" title="LATTICE2:func.3">FinMeet</a> (<font color="Maroon" title="c2">B</font>,<span class="p1">(<span class="default"> the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c1">DL</font> <a href="funcop_1.html#K9" title="FUNCOP_1:func.9">[:]</a> (<span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c1">DL</font></span>)</span>,<font color="Maroon" title="c3">p</font>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattice2.html#D4" title="LATTICE2:def.4">LATTICE2:def 4</a></span>
<br/>.= 
 <a href="lattice2.html#K3" title="LATTICE2:func.3">FinMeet</a> (<font color="Maroon" title="c2">B</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c1">DL</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p2">(<span class="default"> the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c1">DL</font> <a href="funcop_1.html#K9" title="FUNCOP_1:func.9">[:]</a> (<span class="p3">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c1">DL</font></span>)</span>,<font color="Maroon" title="c3">p</font>)</span>)</span></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T17" title="FUNCT_2:th.17">FUNCT_2:17</a></span>
<br/>.= 
 <a href="lattice4.html#K2" title="LATTICE4:func.2">FinMeet</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"> the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c1">DL</font> <a href="funcop_1.html#K9" title="FUNCOP_1:func.9">[:]</a> (<span class="p3">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c1">DL</font></span>)</span>,<font color="Maroon" title="c3">p</font>)</span>)</span> <a href="setwiseo.html#K8" title="SETWISEO:func.8">.:</a> <font color="Maroon" title="c2">B</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattice4.html#T22" target="_self" title="LATTICE4:th.22">Th29</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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