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<b>let </b><font color="Maroon" title="c3">i</font>, <font color="Maroon" title="c4">j</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="yellow_9.html#K3" title="YELLOW_9:func.3">opp+id</a> </span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel21.html#D2" target="_self" title="WAYBEL21:def.2">WAYBEL21:def 2</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">i</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c4">j</font> implies <span class="p1">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="yellow_9.html#K3" title="YELLOW_9:func.3">opp+id</a> </span>)</span> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Maroon" title="c3">i</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="yellow_9.html#K3" title="YELLOW_9:func.3">opp+id</a> </span>)</span> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Maroon" title="c4">j</font> )</span><br/>

<a NAME="E1:32_1_1"/><i><font color="Green" title="E16">A1</font></i>: 
<font color="Maroon" title="c2">F</font> <a href="yellow_9.html#K3" title="YELLOW_9:func.3">opp+id</a>  is  <a href="yellow_0.html#V4" title="YELLOW_0:attr.4">full</a>  <a href="yellow_0.html#M1" title="YELLOW_0:mode.1">SubRelStr</a> of <font color="Maroon" title="c1">T</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a> 
 
<b>by </b><i><a class="ref" href="yellow_9.html#T7" title="YELLOW_9:th.7">YELLOW_9:7</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c5">x</font> = <font color="Maroon" title="c3">i</font>, <font color="Maroon" title="c6">y</font> = <font color="Maroon" title="c4">j</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a> </span>)</span> <b>by </b><i><a class="ref" href="yellow_0.html#T59" title="YELLOW_0:th.59">YELLOW_0:59</a></i>;<br/>
<b>assume </b><a NAME="E3:32_1_1"/>
<font color="Maroon" title="c3">i</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c4">j</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">F</font> <a href="yellow_9.html#K3" title="YELLOW_9:func.3">opp+id</a> </span>)</span> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Maroon" title="c3">i</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="yellow_9.html#K3" title="YELLOW_9:func.3">opp+id</a> </span>)</span> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Maroon" title="c4">j</font></span><br/>

<a NAME="E4:32_1_1"/><b>then </b>
<font color="Maroon" title="c5">x</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c6">y</font>
 
<b>by </b><i><a class="txt" href="#E1:32_1_1"><i><font color="Green" title="E16">A1</font></i></a>, <a class="ref" href="yellow_0.html#T60" title="YELLOW_0:th.60">YELLOW_0:60</a></i>;<br/>
<a NAME="E5:32_1_1"/><b>then </b>
(  <a href="lattice3.html#K9" title="LATTICE3:func.9">~</a> <font color="Maroon" title="c5">x</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a>  <a href="lattice3.html#K9" title="LATTICE3:func.9">~</a> <font color="Maroon" title="c6">y</font> &amp;  <a href="lattice3.html#K9" title="LATTICE3:func.9">~</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">x</font> )
 
<b>by </b><i><a class="ref" href="yellow_7.html#T1" title="YELLOW_7:th.1">YELLOW_7:1</a></i>;<br/>
<a NAME="E6:32_1_1"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="yellow_9.html#K3" title="YELLOW_9:func.3">opp+id</a> </span>)</span> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Maroon" title="c3">i</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a>  <a href="lattice3.html#K9" title="LATTICE3:func.9">~</a> <font color="Maroon" title="c6">y</font> &amp;  <a href="lattice3.html#K9" title="LATTICE3:func.9">~</a> <font color="Maroon" title="c6">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">y</font> )
 
<b>by </b><i><a class="ref" href="yellow_9.html#T7" title="YELLOW_9:th.7">YELLOW_9:7</a></i>;<br/>
<b>hence </b><a NAME="E7:32_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="yellow_9.html#K3" title="YELLOW_9:func.3">opp+id</a> </span>)</span> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Maroon" title="c3">i</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="yellow_9.html#K3" title="YELLOW_9:func.3">opp+id</a> </span>)</span> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Maroon" title="c4">j</font>
 <b>by </b><i><a class="ref" href="yellow_9.html#T7" title="YELLOW_9:th.7">YELLOW_9:7</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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