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<div><span class="kw">theorem </span><a NAME="T24"><span class="comment"><font color="firebrick">:: REAL_LAT:24</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">A</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">p</font>, <font color="Olive" title="b3">q</font>, <font color="Olive" title="b4">r</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#K6" title="REAL_LAT:func.6">RealFunc_Lattice</a> <font color="Olive" title="b1">A</font></span>)</span> holds <br/> ( <span class="p1">(<span class="default"><a href="real_lat.html#K5" title="REAL_LAT:func.5">minfuncreal</a> <font color="Olive" title="b1">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b2">p</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="Olive" title="b1">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b3">q</font>,<font color="Olive" title="b4">r</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="real_lat.html#K5" title="REAL_LAT:func.5">minfuncreal</a> <font color="Olive" title="b1">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="Olive" title="b1">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b3">q</font>,<font color="Olive" title="b4">r</font>)</span>)</span>,<font color="Olive" title="b2">p</font>) &amp; <span class="p1">(<span class="default"><a href="real_lat.html#K5" title="REAL_LAT:func.5">minfuncreal</a> <font color="Olive" title="b1">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b2">p</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="Olive" title="b1">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b3">q</font>,<font color="Olive" title="b4">r</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="real_lat.html#K5" title="REAL_LAT:func.5">minfuncreal</a> <font color="Olive" title="b1">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="Olive" title="b1">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b2">p</font>,<font color="Olive" title="b3">q</font>)</span>)</span>,<font color="Olive" title="b4">r</font>) &amp; <span class="p1">(<span class="default"><a href="real_lat.html#K5" title="REAL_LAT:func.5">minfuncreal</a> <font color="Olive" title="b1">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b2">p</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="Olive" title="b1">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b3">q</font>,<font color="Olive" title="b4">r</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="real_lat.html#K5" title="REAL_LAT:func.5">minfuncreal</a> <font color="Olive" title="b1">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="Olive" title="b1">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b3">q</font>,<font color="Olive" title="b2">p</font>)</span>)</span>,<font color="Olive" title="b4">r</font>) &amp; <span class="p1">(<span class="default"><a href="real_lat.html#K5" title="REAL_LAT:func.5">minfuncreal</a> <font color="Olive" title="b1">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b2">p</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="Olive" title="b1">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b3">q</font>,<font color="Olive" title="b4">r</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="real_lat.html#K5" title="REAL_LAT:func.5">minfuncreal</a> <font color="Olive" title="b1">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="Olive" title="b1">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b4">r</font>,<font color="Olive" title="b2">p</font>)</span>)</span>,<font color="Olive" title="b3">q</font>) &amp; <span class="p1">(<span class="default"><a href="real_lat.html#K5" title="REAL_LAT:func.5">minfuncreal</a> <font color="Olive" title="b1">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b2">p</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="Olive" title="b1">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b3">q</font>,<font color="Olive" title="b4">r</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="real_lat.html#K5" title="REAL_LAT:func.5">minfuncreal</a> <font color="Olive" title="b1">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="Olive" title="b1">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b4">r</font>,<font color="Olive" title="b3">q</font>)</span>)</span>,<font color="Olive" title="b2">p</font>) &amp; <span class="p1">(<span class="default"><a href="real_lat.html#K5" title="REAL_LAT:func.5">minfuncreal</a> <font color="Olive" title="b1">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b2">p</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="Olive" title="b1">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b3">q</font>,<font color="Olive" title="b4">r</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="real_lat.html#K5" title="REAL_LAT:func.5">minfuncreal</a> <font color="Olive" title="b1">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="Olive" title="b1">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b2">p</font>,<font color="Olive" title="b4">r</font>)</span>)</span>,<font color="Olive" title="b3">q</font>) )</div></div>
