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<b>let </b><font color="Maroon" title="c1">A</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> 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 <span class="p1">(<span class="default"><a href="real_lat.html#K7" title="REAL_LAT:func.7">RealFunc_Lattice</a> <font color="Maroon" title="c1">A</font></span>)</span> holds <br/> ( <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> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font></span>)</span>,<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; <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> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b2">q</font>,<span class="p1">(<span class="default"><span class="p2">(<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> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">q</font> &amp; <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> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b2">q</font>,<span class="p1">(<span class="default"><span class="p2">(<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> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b2">q</font>,<font color="Olive" title="b1">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">q</font> &amp; <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> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b2">q</font>,<font color="Olive" title="b1">p</font></span>)</span>,<font color="Olive" title="b2">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">q</font> )</span><br/><b>let </b><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">q</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="real_lat.html#K7" title="REAL_LAT:func.7">RealFunc_Lattice</a> <font color="Maroon" title="c1">A</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <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> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font></span>)</span>,<font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">q</font> &amp; <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> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c3">q</font>,<span class="p1">(<span class="default"><span class="p2">(<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> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">q</font> &amp; <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> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c3">q</font>,<span class="p1">(<span class="default"><span class="p2">(<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> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c2">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">q</font> &amp; <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> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c2">p</font></span>)</span>,<font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">q</font> )</span><br/>





<b>thus </b><a NAME="E1:36"/><i><font color="Green" title="E35">A1</font></i>: 
<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> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font></span>)</span>,<font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">q</font>
 <b>by </b><i><a class="ref" href="real_lat.html#T26" target="_self" title="REAL_LAT:th.26">Th26</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <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> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c3">q</font>,<span class="p1">(<span class="default"><span class="p2">(<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> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">q</font> &amp; <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> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c3">q</font>,<span class="p1">(<span class="default"><span class="p2">(<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> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c2">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">q</font> &amp; <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> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c2">p</font></span>)</span>,<font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">q</font> )</span><br/>

<b>thus </b><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> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c3">q</font>,<span class="p1">(<span class="default"><span class="p2">(<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> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">q</font>
<b>by </b><i><a class="ref" href="lattices.html#D1" title="LATTICES:def.1">LATTICES:def 1</a></i>
<br/>.= 
<font color="Maroon" title="c3">q</font>
<b>by </b><i><a class="ref" href="real_lat.html#T26" target="_self" title="REAL_LAT:th.26">Th26</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <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> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c3">q</font>,<span class="p1">(<span class="default"><span class="p2">(<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> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c2">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">q</font> &amp; <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> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c2">p</font></span>)</span>,<font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">q</font> )</span><br/>

<b>thus </b><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> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c3">q</font>,<span class="p1">(<span class="default"><span class="p2">(<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> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c2">p</font></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> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c3">q</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">q</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c2">p</font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">q</font>
<b>by </b><i><a class="ref" href="lattices.html#D1" title="LATTICES:def.1">LATTICES:def 1</a></i>
<br/>.= 
<font color="Maroon" title="c3">q</font>
<b>by </b><i><a class="ref" href="real_lat.html#T26" target="_self" title="REAL_LAT:th.26">Th26</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <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> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c2">p</font></span>)</span>,<font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">q</font></span><br/>

<b>thus </b><a NAME="E4:36"/>
<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> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<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> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c2">p</font></span>)</span>,<font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">q</font>
 <b>by </b><i><a class="txt" href="#E1:36"><i><font color="Green" title="E35">A1</font></i></a>, <a class="ref" href="real_lat.html#T41" target="_self" title="REAL_LAT:th.41">Th41</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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