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<b>set </b><font color="Maroon" title="c3">s</font> = <font color="Maroon" title="c2">R</font> <a href="waybel35.html#K1" title="WAYBEL35:func.1">-LowerMap</a> ;<br/>
<b>let </b><font color="Maroon" title="c4">x</font>, <font color="Maroon" title="c5">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_1.html#D2" title="WAYBEL_1:def.2">WAYBEL_1:def 2</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="c4">x</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c5">y</font> or <span class="p1">(<span class="default"><font color="Maroon" title="c2">R</font> <a href="waybel35.html#K1" title="WAYBEL35:func.1">-LowerMap</a> </span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">x</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">R</font> <a href="waybel35.html#K1" title="WAYBEL35:func.1">-LowerMap</a> </span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">y</font> )</span><br/>

<a NAME="E1:18_1_1"/><i><font color="Green" title="E5">A1</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon" title="c2">R</font> <a href="waybel35.html#K1" title="WAYBEL35:func.1">-LowerMap</a> </span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">R</font> <a href="waybel_4.html#K5" title="WAYBEL_4:func.5">-below</a> <font color="Maroon" title="c4">x</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">R</font> <a href="waybel35.html#K1" title="WAYBEL35:func.1">-LowerMap</a> </span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">R</font> <a href="waybel_4.html#K5" title="WAYBEL_4:func.5">-below</a> <font color="Maroon" title="c5">y</font> )
 
<b>by </b><i><a class="ref" href="waybel35.html#D2" target="_self" title="WAYBEL35:def.2">Def2</a></i>;<br/>
<b>assume </b><a NAME="E2:18_1_1"/>
<font color="Maroon" title="c4">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">y</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"><font color="Maroon" title="c2">R</font> <a href="waybel35.html#K1" title="WAYBEL35:func.1">-LowerMap</a> </span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">x</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">R</font> <a href="waybel35.html#K1" title="WAYBEL35:func.1">-LowerMap</a> </span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">y</font></span><br/>

<a NAME="E3:18_1_1"/><b>then </b>
<font color="Maroon" title="c2">R</font> <a href="waybel_4.html#K5" title="WAYBEL_4:func.5">-below</a> <font color="Maroon" title="c4">x</font> <a href="lattice7.html#R1" title="LATTICE7:pred.1">c=</a> <font color="Maroon" title="c2">R</font> <a href="waybel_4.html#K5" title="WAYBEL_4:func.5">-below</a> <font color="Maroon" title="c5">y</font>
 
<b>by </b><i><a class="ref" href="waybel_4.html#T17" title="WAYBEL_4:th.17">WAYBEL_4:17</a></i>;<br/>
<b>hence </b><a NAME="E4:18_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">R</font> <a href="waybel35.html#K1" title="WAYBEL35:func.1">-LowerMap</a> </span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">x</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">R</font> <a href="waybel35.html#K1" title="WAYBEL35:func.1">-LowerMap</a> </span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">y</font>
 <b>by </b><i><a class="txt" href="waybel35.html#E1:18_1_1"><i><font color="Green" title="E5">A1</font></i></a>, <a class="ref" href="yellow_1.html#T3" title="YELLOW_1:th.3">YELLOW_1:3</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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