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<div class="add">

<b>let </b><font color="Maroon" title="c1">S</font>, <font color="Maroon" title="c2">T</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">g</font> being <a href="waybel_0.html#V17" title="WAYBEL_0:attr.17">infs-preserving</a> <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">T</font><br/> for <font color="Olive" title="b2">X</font> being <a href="waybel11.html#V4" title="WAYBEL11:attr.4">Scott</a>  <a href="yellow_9.html#M1" title="YELLOW_9:mode.1">TopAugmentation</a> of <font color="Maroon" title="c2">T</font><br/> for <font color="Olive" title="b3">Y</font> being <a href="waybel11.html#V4" title="WAYBEL11:attr.4">Scott</a>  <a href="yellow_9.html#M1" title="YELLOW_9:mode.1">TopAugmentation</a> of <font color="Maroon" title="c1">S</font><br/> for <font color="Olive" title="b4">V</font> being <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b2">X</font> holds  <span class="p1">(<span class="default"><a href="waybel34.html#K1" title="WAYBEL34:func.1">LowerAdj</a> <font color="Olive" title="b1">g</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Olive" title="b4">V</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p2">(<span class="default"><a href="waybel34.html#K1" title="WAYBEL34:func.1">LowerAdj</a> <font color="Olive" title="b1">g</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K4" title="WAYBEL_0:func.4">uparrow</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="waybel34.html#K1" title="WAYBEL34:func.1">LowerAdj</a> <font color="Olive" title="b1">g</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Olive" title="b4">V</font></span>)</span></span>)</span></span><br/><b>let </b><font color="Maroon" title="c3">g</font> be  <a href="waybel_0.html#V17" title="WAYBEL_0:attr.17">infs-preserving</a> <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">T</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">X</font> being <a href="waybel11.html#V4" title="WAYBEL11:attr.4">Scott</a>  <a href="yellow_9.html#M1" title="YELLOW_9:mode.1">TopAugmentation</a> of <font color="Maroon" title="c2">T</font><br/> for <font color="Olive" title="b2">Y</font> being <a href="waybel11.html#V4" title="WAYBEL11:attr.4">Scott</a>  <a href="yellow_9.html#M1" title="YELLOW_9:mode.1">TopAugmentation</a> of <font color="Maroon" title="c1">S</font><br/> for <font color="Olive" title="b3">V</font> being <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">X</font> holds  <span class="p1">(<span class="default"><a href="waybel34.html#K1" title="WAYBEL34:func.1">LowerAdj</a> <font color="Maroon" title="c3">g</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Olive" title="b3">V</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p2">(<span class="default"><a href="waybel34.html#K1" title="WAYBEL34:func.1">LowerAdj</a> <font color="Maroon" title="c3">g</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K4" title="WAYBEL_0:func.4">uparrow</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="waybel34.html#K1" title="WAYBEL34:func.1">LowerAdj</a> <font color="Maroon" title="c3">g</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Olive" title="b3">V</font></span>)</span></span>)</span></span><br/><b>let </b><font color="Maroon" title="c4">X</font> be  <a href="waybel11.html#V4" title="WAYBEL11:attr.4">Scott</a>  <a href="yellow_9.html#M1" title="YELLOW_9:mode.1">TopAugmentation</a> of <font color="Maroon" title="c2">T</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">Y</font> being <a href="waybel11.html#V4" title="WAYBEL11:attr.4">Scott</a>  <a href="yellow_9.html#M1" title="YELLOW_9:mode.1">TopAugmentation</a> of <font color="Maroon" title="c1">S</font><br/> for <font color="Olive" title="b2">V</font> being <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c4">X</font> holds  <span class="p1">(<span class="default"><a href="waybel34.html#K1" title="WAYBEL34:func.1">LowerAdj</a> <font color="Maroon" title="c3">g</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Olive" title="b2">V</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p2">(<span class="default"><a href="waybel34.html#K1" title="WAYBEL34:func.1">LowerAdj</a> <font color="Maroon" title="c3">g</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K4" title="WAYBEL_0:func.4">uparrow</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="waybel34.html#K1" title="WAYBEL34:func.1">LowerAdj</a> <font color="Maroon" title="c3">g</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Olive" title="b2">V</font></span>)</span></span>)</span></span><br/><b>let </b><font color="Maroon" title="c5">Y</font> be  <a href="waybel11.html#V4" title="WAYBEL11:attr.4">Scott</a>  <a href="yellow_9.html#M1" title="YELLOW_9:mode.1">TopAugmentation</a> of <font color="Maroon" title="c1">S</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">V</font> being <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c4">X</font> holds  <span class="p1">(<span class="default"><a href="waybel34.html#K1" title="WAYBEL34:func.1">LowerAdj</a> <font color="Maroon" title="c3">g</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Olive" title="b1">V</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p2">(<span class="default"><a href="waybel34.html#K1" title="WAYBEL34:func.1">LowerAdj</a> <font color="Maroon" title="c3">g</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K4" title="WAYBEL_0:func.4">uparrow</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="waybel34.html#K1" title="WAYBEL34:func.1">LowerAdj</a> <font color="Maroon" title="c3">g</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Olive" title="b1">V</font></span>)</span></span>)</span></span><br/>







<a NAME="E1:44"/><i><font color="Green" title="E31">A1</font></i>: 
(  <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">X</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c4">X</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">T</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">T</font> #) &amp;  <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c5">Y</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c5">Y</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">S</font> #) )
 
<b>by </b><i><a class="ref" href="yellow_9.html#D4" title="YELLOW_9:def.4">YELLOW_9:def 4</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c6">d</font> =  <a href="waybel34.html#K1" title="WAYBEL34:func.1">LowerAdj</a> <font color="Maroon" title="c3">g</font> as   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c5">Y</font> ;<br/>
<b>let </b><font color="Maroon" title="c7">V</font> be  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c4">X</font>; <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="waybel34.html#K1" title="WAYBEL34:func.1">LowerAdj</a> <font color="Maroon" title="c3">g</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c7">V</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p2">(<span class="default"><a href="waybel34.html#K1" title="WAYBEL34:func.1">LowerAdj</a> <font color="Maroon" title="c3">g</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K4" title="WAYBEL_0:func.4">uparrow</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="waybel34.html#K1" title="WAYBEL34:func.1">LowerAdj</a> <font color="Maroon" title="c3">g</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c7">V</font></span>)</span></span>)</span></span><br/>

<b>reconsider </b><font color="Maroon" title="c8">A</font> =  <a href="waybel_0.html#K4" title="WAYBEL_0:func.4">uparrow</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="waybel34.html#K1" title="WAYBEL34:func.1">LowerAdj</a> <font color="Maroon" title="c3">g</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c7">V</font></span>)</span> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c5">Y</font> <b>by </b><i><a class="txt" href="#E1:44"><i><font color="Green" title="E31">A1</font></i></a></i>;<br/>
<a NAME="E4:44"/>
<font color="Maroon" title="c6">d</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c7">V</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c6">d</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="44_1"><b>proof </b></a><div class="add">

<a NAME="E1:44_1"/>
( <font color="Maroon" title="c6">d</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c7">V</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c8">A</font> &amp; <font color="Maroon" title="c6">d</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c7">V</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c6">d</font> )
 
<b>by </b><i><a class="ref" href="relat_1.html#T144" title="RELAT_1:th.144">RELAT_1:144</a>, <a class="ref" href="waybel_0.html#T16" title="WAYBEL_0:th.16">WAYBEL_0:16</a></i>;<br/>
<b>hence </b><a NAME="E2:44_1"/>
<font color="Maroon" title="c6">d</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c7">V</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c8">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c6">d</font></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T19" title="XBOOLE_1:th.19">XBOOLE_1:19</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c8">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c6">d</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">d</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c7">V</font></span><br/>

<b>let </b><font color="Maroon" title="c9">t</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c9">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c6">d</font></span>)</span> or <font color="Maroon" title="c9">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">d</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c7">V</font> )</span><br/>

<b>assume </b><a NAME="E3:44_1"/>
<font color="Maroon" title="c9">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c6">d</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c9">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">d</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c7">V</font></span><br/>

<a NAME="E4:44_1"/><b>then </b><i><font color="Green" title="E32">A2</font></i>: 
( <font color="Maroon" title="c9">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">A</font> &amp; <font color="Maroon" title="c9">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c6">d</font> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c10">t</font> = <font color="Maroon" title="c9">t</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">S</font> ;<br/>
<b>consider </b><font color="Maroon" title="c11">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">S</font><b> such that </b><br/><a NAME="E7:44_1"/><i><font color="Green" title="E33">A3</font></i>: 
( <font color="Maroon" title="c11">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c10">t</font> &amp; <font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="waybel34.html#K1" title="WAYBEL34:func.1">LowerAdj</a> <font color="Maroon" title="c3">g</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c7">V</font> )
 <b>by </b><i><a class="txt" href="#E4:44_1"><i><font color="Green" title="E32">A2</font></i></a>, <a class="ref" href="waybel_0.html#D16" title="WAYBEL_0:def.16">WAYBEL_0:def 16</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c12">u</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E9:44_1"/><i><font color="Green" title="E34">A4</font></i>: 
( <font color="Maroon" title="c12">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">T</font> &amp; <font color="Maroon" title="c12">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">V</font> &amp; <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="waybel34.html#K1" title="WAYBEL34:func.1">LowerAdj</a> <font color="Maroon" title="c3">g</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">u</font> )
 <b>by </b><i><a class="txt" href="#E7:44_1"><i><font color="Green" title="E33">A3</font></i></a>, <a class="ref" href="funct_2.html#T115" title="FUNCT_2:th.115">FUNCT_2:115</a></i>;<br/>
<a NAME="E10:44_1"/>
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c6">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">T</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c13">v</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E12:44_1"/><i><font color="Green" title="E35">A5</font></i>: 
( <font color="Maroon" title="c13">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">T</font> &amp; <font color="Maroon" title="c10">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">v</font> )
 <b>by </b><i><a class="txt" href="#E4:44_1"><i><font color="Green" title="E32">A2</font></i></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c14">u</font> = <font color="Maroon" title="c12">u</font>, <font color="Maroon" title="c15">v</font> = <font color="Maroon" title="c13">v</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">T</font> <b>by </b><i><a class="txt" href="#E9:44_1"><i><font color="Green" title="E34">A4</font></i></a>, <a class="txt" href="#E12:44_1"><i><font color="Green" title="E35">A5</font></i></a></i>;<br/>
<i><font color="Green" title="E36">A6</font></i>: <span class="p1">(<span class="default"><a href="waybel34.html#K1" title="WAYBEL34:func.1">LowerAdj</a> <font color="Maroon" title="c3">g</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">u</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c15">v</font></span>)</span> = 
<font color="Maroon" title="c11">x</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c10">t</font>
<b>by </b><i><a class="txt" href="#E9:44_1"><i><font color="Green" title="E34">A4</font></i></a>, <a class="txt" href="#E12:44_1"><i><font color="Green" title="E35">A5</font></i></a>, <a class="ref" href="waybel_6.html#T2" title="WAYBEL_6:th.2">WAYBEL_6:2</a></i>
<br/>.= 
<font color="Maroon" title="c10">t</font>
<b>by </b><i><a class="txt" href="#E7:44_1"><i><font color="Green" title="E33">A3</font></i></a>, <a class="ref" href="yellow_0.html#T24" title="YELLOW_0:th.24">YELLOW_0:24</a></i>
;<br/>
<b>reconsider </b><font color="Maroon" title="c16">V'</font> = <font color="Maroon" title="c7">V</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">T</font> <b>by </b><i><a class="txt" href="#E1:44"><i><font color="Green" title="E31">A1</font></i></a></i>;<br/>
<a NAME="E16:44_1"/>
<font color="Maroon" title="c7">V</font> is <a href="waybel_0.html#V13" title="WAYBEL_0:attr.13">upper</a>
 
<b>by </b><i><a class="ref" href="waybel11.html#D4" title="WAYBEL11:def.4">WAYBEL11:def 4</a></i>;<br/>
<a NAME="E17:44_1"/><b>then </b>
( <font color="Maroon" title="c16">V'</font> is <a href="waybel_0.html#V13" title="WAYBEL_0:attr.13">upper</a> &amp; <font color="Maroon" title="c14">u</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c14">u</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c15">v</font> )
 
<b>by </b><i><a class="txt" href="#E1:44"><i><font color="Green" title="E31">A1</font></i></a>, <a class="ref" href="waybel_0.html#T25" title="WAYBEL_0:th.25">WAYBEL_0:25</a>, <a class="ref" href="yellow_0.html#T22" title="YELLOW_0:th.22">YELLOW_0:22</a></i>;<br/>
<a NAME="E18:44_1"/><b>then </b>
<font color="Maroon" title="c14">u</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c15">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c16">V'</font>
 
<b>by </b><i><a class="txt" href="#E9:44_1"><i><font color="Green" title="E34">A4</font></i></a>, <a class="ref" href="waybel_0.html#D20" title="WAYBEL_0:def.20">WAYBEL_0:def 20</a></i>;<br/>
<b>hence </b><a NAME="E19:44_1"/>
<font color="Maroon" title="c9">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">d</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c7">V</font>
 <b>by </b><i><a class="txt" href="#E14:44_1"><i><font color="Green" title="E36">A6</font></i></a>, <a class="ref" href="funct_2.html#T43" title="FUNCT_2:th.43">FUNCT_2:43</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E5:44"/>
<span class="p1">(<span class="default"><a href="waybel34.html#K1" title="WAYBEL34:func.1">LowerAdj</a> <font color="Maroon" title="c3">g</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c7">V</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p2">(<span class="default"><a href="waybel34.html#K1" title="WAYBEL34:func.1">LowerAdj</a> <font color="Maroon" title="c3">g</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K4" title="WAYBEL_0:func.4">uparrow</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="waybel34.html#K1" title="WAYBEL34:func.1">LowerAdj</a> <font color="Maroon" title="c3">g</font></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c7">V</font></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
