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<b>set </b><font color="Maroon" title="c4">I</font> = <font color="Maroon" title="c3">AR</font> <a href="waybel_4.html#K5" title="WAYBEL_4:func.5">-below</a> <font color="Maroon" title="c2">x</font>;<br/>
<b>let </b><font color="Maroon" title="c5">u1</font>, <font color="Maroon" title="c6">u2</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_0.html#D1" title="WAYBEL_0:def.1">WAYBEL_0:def 1</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="c5">u1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">AR</font> <a href="waybel_4.html#K5" title="WAYBEL_4:func.5">-below</a> <font color="Maroon" title="c2">x</font> or  not <font color="Maroon" title="c6">u2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">AR</font> <a href="waybel_4.html#K5" title="WAYBEL_4:func.5">-below</a> <font color="Maroon" title="c2">x</font> or  ex <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">AR</font> <a href="waybel_4.html#K5" title="WAYBEL_4:func.5">-below</a> <font color="Maroon" title="c2">x</font> &amp; <font color="Maroon" title="c5">u1</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon" title="c6">u2</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> ) )</span><br/>

<b>assume </b><a NAME="E1:38_1_1"/><i><font color="Green" title="E21">A1</font></i>: 
( <font color="Maroon" title="c5">u1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">AR</font> <a href="waybel_4.html#K5" title="WAYBEL_4:func.5">-below</a> <font color="Maroon" title="c2">x</font> &amp; <font color="Maroon" title="c6">u2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">AR</font> <a href="waybel_4.html#K5" title="WAYBEL_4:func.5">-below</a> <font color="Maroon" title="c2">x</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">AR</font> <a href="waybel_4.html#K5" title="WAYBEL_4:func.5">-below</a> <font color="Maroon" title="c2">x</font> &amp; <font color="Maroon" title="c5">u1</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon" title="c6">u2</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> )</span><br/>

<b>then consider </b><font color="Maroon" title="c7">v1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font><b> such that </b><br/><a NAME="E3:38_1_1"/><i><font color="Green" title="E22">A2</font></i>: 
( <font color="Maroon" title="c7">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">u1</font> &amp; <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c7">v1</font>,<font color="Maroon" title="c2">x</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">AR</font> )
 ;<br/>
<b>consider </b><font color="Maroon" title="c8">v2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font><b> such that </b><br/><a NAME="E5:38_1_1"/><i><font color="Green" title="E23">A3</font></i>: 
( <font color="Maroon" title="c8">v2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">u2</font> &amp; <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c8">v2</font>,<font color="Maroon" title="c2">x</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">AR</font> )
 <b>by </b><i><a class="txt" href="#E1:38_1_1"><i><font color="Green" title="E21">A1</font></i></a></i>;<br/>
<b>take </b><font color="Maroon" title="c9">u12</font> = <font color="Maroon" title="c5">u1</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c6">u2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c9">u12</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">AR</font> <a href="waybel_4.html#K5" title="WAYBEL_4:func.5">-below</a> <font color="Maroon" title="c2">x</font> &amp; <font color="Maroon" title="c5">u1</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c9">u12</font> &amp; <font color="Maroon" title="c6">u2</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c9">u12</font> )</span><br/>

<a NAME="E6:38_1_1"/>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c9">u12</font>,<font color="Maroon" title="c2">x</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">AR</font>
 
<b>by </b><i><a class="txt" href="#E3:38_1_1"><i><font color="Green" title="E22">A2</font></i></a>, <a class="txt" href="#E5:38_1_1"><i><font color="Green" title="E23">A3</font></i></a>, <a class="ref" href="waybel_4.html#D6" target="_self" title="WAYBEL_4:def.6">Def6</a></i>;<br/>
<b>hence </b><a NAME="E7:38_1_1"/>
( <font color="Maroon" title="c9">u12</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">AR</font> <a href="waybel_4.html#K5" title="WAYBEL_4:func.5">-below</a> <font color="Maroon" title="c2">x</font> &amp; <font color="Maroon" title="c5">u1</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c9">u12</font> &amp; <font color="Maroon" title="c6">u2</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c9">u12</font> )
 <b>by </b><i><a class="ref" href="yellow_0.html#T22" title="YELLOW_0:th.22">YELLOW_0:22</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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