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<b>let </b><font color="Maroon" title="c1">L1</font>, <font color="Maroon" title="c2">L2</font>, <font color="Maroon" title="c3">L3</font> be  <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a> <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">LATTICE</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">d1</font> being <a href="waybel_0.html#V18" title="WAYBEL_0:attr.18">sups-preserving</a> <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">L1</font>,<font color="Maroon" title="c2">L2</font><br/> for <font color="Olive" title="b2">d2</font> being <a href="waybel_0.html#V18" title="WAYBEL_0:attr.18">sups-preserving</a> <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">L2</font>,<font color="Maroon" title="c3">L3</font> holds   <a href="waybel34.html#K2" title="WAYBEL34:func.2">UpperAdj</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">d2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b1">d1</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><a href="waybel34.html#K2" title="WAYBEL34:func.2">UpperAdj</a> <font color="Olive" title="b1">d1</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><a href="waybel34.html#K2" title="WAYBEL34:func.2">UpperAdj</a> <font color="Olive" title="b2">d2</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c4">d1</font> be  <a href="waybel_0.html#V18" title="WAYBEL_0:attr.18">sups-preserving</a> <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">L1</font>,<font color="Maroon" title="c2">L2</font>; <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">d2</font> being <a href="waybel_0.html#V18" title="WAYBEL_0:attr.18">sups-preserving</a> <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">L2</font>,<font color="Maroon" title="c3">L3</font> holds   <a href="waybel34.html#K2" title="WAYBEL34:func.2">UpperAdj</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">d2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">d1</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><a href="waybel34.html#K2" title="WAYBEL34:func.2">UpperAdj</a> <font color="Maroon" title="c4">d1</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><a href="waybel34.html#K2" title="WAYBEL34:func.2">UpperAdj</a> <font color="Olive" title="b1">d2</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c5">d2</font> be  <a href="waybel_0.html#V18" title="WAYBEL_0:attr.18">sups-preserving</a> <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">L2</font>,<font color="Maroon" title="c3">L3</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="waybel34.html#K2" title="WAYBEL34:func.2">UpperAdj</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">d2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">d1</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><a href="waybel34.html#K2" title="WAYBEL34:func.2">UpperAdj</a> <font color="Maroon" title="c4">d1</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><a href="waybel34.html#K2" title="WAYBEL34:func.2">UpperAdj</a> <font color="Maroon" title="c5">d2</font></span>)</span></span><br/>





<a NAME="E1:19"/>
( <span class="p1"><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><a href="waybel34.html#K2" title="WAYBEL34:func.2">UpperAdj</a> <font color="Maroon" title="c4">d1</font></span>)</span>,<font color="Maroon" title="c4">d1</font></span><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">]</a></span> is <a href="waybel_1.html#V3" title="WAYBEL_1:attr.3">Galois</a> &amp; <span class="p1"><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><a href="waybel34.html#K2" title="WAYBEL34:func.2">UpperAdj</a> <font color="Maroon" title="c5">d2</font></span>)</span>,<font color="Maroon" title="c5">d2</font></span><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">]</a></span> is <a href="waybel_1.html#V3" title="WAYBEL_1:attr.3">Galois</a> )
 
<b>by </b><i><a class="ref" href="waybel34.html#D2" target="_self" title="WAYBEL34:def.2">Def2</a></i>;<br/>
<a NAME="E2:19"/><b>then </b>
( <span class="p1"><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="waybel34.html#K2" title="WAYBEL34:func.2">UpperAdj</a> <font color="Maroon" title="c4">d1</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p3">(<span class="default"><a href="waybel34.html#K2" title="WAYBEL34:func.2">UpperAdj</a> <font color="Maroon" title="c5">d2</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">d2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">d1</font></span>)</span></span><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">]</a></span> is <a href="waybel_1.html#V3" title="WAYBEL_1:attr.3">Galois</a> &amp; <font color="Maroon" title="c5">d2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">d1</font> is <a href="waybel_0.html#V18" title="WAYBEL_0:attr.18">sups-preserving</a> )
 
<b>by </b><i><a class="ref" href="waybel15.html#T7" title="WAYBEL15:th.7">WAYBEL15:7</a>, <a class="ref" href="waybel20.html#T28" title="WAYBEL20:th.28">WAYBEL20:28</a></i>;<br/>
<b>hence </b><a NAME="E3:19"/>
 <a href="waybel34.html#K2" title="WAYBEL34:func.2">UpperAdj</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">d2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">d1</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><a href="waybel34.html#K2" title="WAYBEL34:func.2">UpperAdj</a> <font color="Maroon" title="c4">d1</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><a href="waybel34.html#K2" title="WAYBEL34:func.2">UpperAdj</a> <font color="Maroon" title="c5">d2</font></span>)</span>
 <b>by </b><i><a class="ref" href="waybel34.html#D2" target="_self" title="WAYBEL34:def.2">Def2</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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