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<span class="kw">let </span><font color="Maroon" title="c1">0L</font> be   <a href="lattices.html#V13" title="LATTICES:attr.13">lower-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">B1</font>, <font color="Olive" title="b2">B2</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">0L</font> holds  <span class="p1">(<span class="default"><a href="lattice4.html#K1" title="LATTICE4:func.1">FinJoin</a> <font color="Olive" title="b1">B1</font></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><a href="lattice4.html#K1" title="LATTICE4:func.1">FinJoin</a> <font color="Olive" title="b2">B2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattice4.html#K1" title="LATTICE4:func.1">FinJoin</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">B1</font> <a href="setwiseo.html#K5" title="SETWISEO:func.5">\/</a> <font color="Olive" title="b2">B2</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">B1</font>, <font color="Maroon" title="c3">B2</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">0L</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#K1" title="LATTICE4:func.1">FinJoin</a> <font color="Maroon" title="c2">B1</font></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><a href="lattice4.html#K1" title="LATTICE4:func.1">FinJoin</a> <font color="Maroon" title="c3">B2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattice4.html#K1" title="LATTICE4:func.1">FinJoin</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B1</font> <a href="setwiseo.html#K5" title="SETWISEO:func.5">\/</a> <font color="Maroon" title="c3">B2</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">0L</font>;<br/>
<span class="kw">thus </span> <a href="lattice4.html#K1" title="LATTICE4:func.1">FinJoin</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B1</font> <a href="setwiseo.html#K5" title="SETWISEO:func.5">\/</a> <font color="Maroon" title="c3">B2</font></span>)</span> = 
 the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c1">0L</font> <a href="setwiseo.html#K7" title="SETWISEO:func.7">$$</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">B1</font> <a href="setwiseo.html#K5" title="SETWISEO:func.5">\/</a> <font color="Maroon" title="c3">B2</font></span>)</span>,<span class="p1">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c1">0L</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattice2.html#D3" title="LATTICE2:def.3">LATTICE2:def 3</a></span>
<br/>.= 
<span class="p1">(<span class="default"> the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c1">0L</font> <a href="setwiseo.html#K7" title="SETWISEO:func.7">$$</a> (<font color="Maroon" title="c2">B1</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">0L</font></span>)</span>)</span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <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">0L</font> <a href="setwiseo.html#K7" title="SETWISEO:func.7">$$</a> (<font color="Maroon" title="c3">B2</font>,<span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c1">0L</font></span>)</span>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="setwiseo.html#T33" title="SETWISEO:th.33">SETWISEO:33</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="lattice4.html#K1" title="LATTICE4:func.1">FinJoin</a> <font color="Maroon" title="c2">B1</font></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"> the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c1">0L</font> <a href="setwiseo.html#K7" title="SETWISEO:func.7">$$</a> (<font color="Maroon" title="c3">B2</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">0L</font></span>)</span>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattice2.html#D3" title="LATTICE2:def.3">LATTICE2:def 3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="lattice4.html#K1" title="LATTICE4:func.1">FinJoin</a> <font color="Maroon" title="c2">B1</font></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><a href="lattice4.html#K1" title="LATTICE4:func.1">FinJoin</a> <font color="Maroon" title="c3">B2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattice2.html#D3" title="LATTICE2:def.3">LATTICE2:def 3</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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