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<a NAME="E1:38_1_1"/>
 <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon" title="c1">A</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> </span>)</span>,<span class="p1">(<span class="default"><a href="real_lat.html#K4" title="REAL_LAT:func.4">maxfuncreal</a> <font color="Maroon" title="c1">A</font></span>)</span>,<span class="p1">(<span class="default"><a href="real_lat.html#K5" title="REAL_LAT:func.5">minfuncreal</a> <font color="Maroon" title="c1">A</font></span>)</span> #) is <a href="lattices.html#V10" title="LATTICES:attr.10">Lattice-like</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="38_1_1_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:38_1_1_1"/>
( ( for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon" title="c1">A</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> </span>)</span>,<span class="p1">(<span class="default"><a href="real_lat.html#K4" title="REAL_LAT:func.4">maxfuncreal</a> <font color="Maroon" title="c1">A</font></span>)</span>,<span class="p1">(<span class="default"><a href="real_lat.html#K5" title="REAL_LAT:func.5">minfuncreal</a> <font color="Maroon" title="c1">A</font></span>)</span> #) holds  <font color="Olive" title="b1">p</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Olive" title="b2">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">q</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Olive" title="b1">p</font> ) &amp; ( for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font>, <font color="Olive" title="b3">r</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon" title="c1">A</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> </span>)</span>,<span class="p1">(<span class="default"><a href="real_lat.html#K4" title="REAL_LAT:func.4">maxfuncreal</a> <font color="Maroon" title="c1">A</font></span>)</span>,<span class="p1">(<span class="default"><a href="real_lat.html#K5" title="REAL_LAT:func.5">minfuncreal</a> <font color="Maroon" title="c1">A</font></span>)</span> #) holds  <font color="Olive" title="b1">p</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">q</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Olive" title="b3">r</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">p</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Olive" title="b2">q</font></span>)</span> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Olive" title="b3">r</font> ) &amp; ( for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon" title="c1">A</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> </span>)</span>,<span class="p1">(<span class="default"><a href="real_lat.html#K4" title="REAL_LAT:func.4">maxfuncreal</a> <font color="Maroon" title="c1">A</font></span>)</span>,<span class="p1">(<span class="default"><a href="real_lat.html#K5" title="REAL_LAT:func.5">minfuncreal</a> <font color="Maroon" title="c1">A</font></span>)</span> #) holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">p</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Olive" title="b2">q</font></span>)</span> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Olive" title="b2">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">q</font> ) &amp; ( for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon" title="c1">A</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> </span>)</span>,<span class="p1">(<span class="default"><a href="real_lat.html#K4" title="REAL_LAT:func.4">maxfuncreal</a> <font color="Maroon" title="c1">A</font></span>)</span>,<span class="p1">(<span class="default"><a href="real_lat.html#K5" title="REAL_LAT:func.5">minfuncreal</a> <font color="Maroon" title="c1">A</font></span>)</span> #) holds  <font color="Olive" title="b1">p</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Olive" title="b2">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">q</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Olive" title="b1">p</font> ) &amp; ( for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font>, <font color="Olive" title="b3">r</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon" title="c1">A</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> </span>)</span>,<span class="p1">(<span class="default"><a href="real_lat.html#K4" title="REAL_LAT:func.4">maxfuncreal</a> <font color="Maroon" title="c1">A</font></span>)</span>,<span class="p1">(<span class="default"><a href="real_lat.html#K5" title="REAL_LAT:func.5">minfuncreal</a> <font color="Maroon" title="c1">A</font></span>)</span> #) holds  <font color="Olive" title="b1">p</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">q</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Olive" title="b3">r</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">p</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Olive" title="b2">q</font></span>)</span> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Olive" title="b3">r</font> ) &amp; ( for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon" title="c1">A</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> </span>)</span>,<span class="p1">(<span class="default"><a href="real_lat.html#K4" title="REAL_LAT:func.4">maxfuncreal</a> <font color="Maroon" title="c1">A</font></span>)</span>,<span class="p1">(<span class="default"><a href="real_lat.html#K5" title="REAL_LAT:func.5">minfuncreal</a> <font color="Maroon" title="c1">A</font></span>)</span> #) holds  <font color="Olive" title="b1">p</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">p</font> <a href="lattices.html#K1" title="LATTICES:func.1">"\/"</a> <font color="Olive" title="b2">q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">p</font> ) )
 <b>by </b><i><a class="ref" href="real_lat.html#T20" target="_self" title="REAL_LAT:th.20">Th20</a>, <a class="ref" href="real_lat.html#T21" target="_self" title="REAL_LAT:th.21">Th21</a>, <a class="ref" href="real_lat.html#T22" target="_self" title="REAL_LAT:th.22">Th22</a>, <a class="ref" href="real_lat.html#T23" target="_self" title="REAL_LAT:th.23">Th23</a>, <a class="ref" href="real_lat.html#T26" target="_self" title="REAL_LAT:th.26">Th26</a>, <a class="ref" href="real_lat.html#T28" target="_self" title="REAL_LAT:th.28">Th28</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="lattices.html#D4" title="LATTICES:def.4">LATTICES:def 4</a>,<a class="ref" href="lattices.html#D5" title="LATTICES:def.5">LATTICES:def 5</a>,<a class="ref" href="lattices.html#D6" title="LATTICES:def.6">LATTICES:def 6</a>,<a class="ref" href="lattices.html#D7" title="LATTICES:def.7">LATTICES:def 7</a>,<a class="ref" href="lattices.html#D8" title="LATTICES:def.8">LATTICES:def 8</a>,<a class="ref" href="lattices.html#D9" title="LATTICES:def.9">LATTICES:def 9</a>,<a class="ref" href="lattices.html#D10" title="LATTICES:def.10">LATTICES:def 10</a><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:38_1_1"/>
 <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon" title="c1">A</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> </span>)</span>,<span class="p1">(<span class="default"><a href="real_lat.html#K4" title="REAL_LAT:func.4">maxfuncreal</a> <font color="Maroon" title="c1">A</font></span>)</span>,<span class="p1">(<span class="default"><a href="real_lat.html#K5" title="REAL_LAT:func.5">minfuncreal</a> <font color="Maroon" title="c1">A</font></span>)</span> #) is  <a href="lattices.html#V3" title="LATTICES:attr.3">strict</a> <a href="lattices.html#NM1" title="LATTICES:NM.1">Lattice</a>
 ;<br/>


</div>
