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<b>let </b><font color="Maroon" title="c1">R1</font>, <font color="Maroon" title="c2">R2</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</a>  <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <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">R1</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">R1</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">R2</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">R2</font> #) implies for <font color="Olive" title="b1">D</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">R1</font><br/> for <font color="Olive" title="b2">D'</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">R2</font>  st <font color="Olive" title="b1">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">D'</font> &amp; <font color="Olive" title="b1">D</font> is <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a> holds <br/><font color="Olive" title="b2">D'</font> is <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a> )</span><br/>

<b>assume </b><a NAME="E1:85"/><i><font color="Green" title="E55">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="c1">R1</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">R1</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">R2</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">R2</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">D</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">R1</font><br/> for <font color="Olive" title="b2">D'</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">R2</font>  st <font color="Olive" title="b1">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">D'</font> &amp; <font color="Olive" title="b1">D</font> is <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a> holds <br/><font color="Olive" title="b2">D'</font> is <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a></span><br/>

<b>let </b><font color="Maroon" title="c3">D</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">R1</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">D'</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">R2</font>  st <font color="Maroon" title="c3">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">D'</font> &amp; <font color="Maroon" title="c3">D</font> is <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a> holds <br/><font color="Olive" title="b1">D'</font> is <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a></span><br/><b>let </b><font color="Maroon" title="c4">D'</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">R2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">D'</font> &amp; <font color="Maroon" title="c3">D</font> is <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a> implies <font color="Maroon" title="c4">D'</font> is <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a> )</span><br/>



<b>assume </b><b>that </b><br/><a NAME="E2:85"/><i><font color="Green" title="E56">A2</font></i>: 
<font color="Maroon" title="c3">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">D'</font>
 <b>and </b><br/><a NAME="E3:85"/><i><font color="Green" title="E57">A3</font></i>: 
<font color="Maroon" title="c3">D</font> is <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">D'</font> is <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a></span><br/>

<b>let </b><font color="Maroon" title="c5">x2</font>, <font color="Maroon" title="c6">y2</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">R2</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">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">D'</font> or  not <font color="Maroon" title="c6">y2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">D'</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="c2">R2</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="c4">D'</font> &amp; <font color="Maroon" title="c5">x2</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">y2</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="E4:85"/><i><font color="Green" title="E58">A4</font></i>: 
( <font color="Maroon" title="c5">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">D'</font> &amp; <font color="Maroon" title="c6">y2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">D'</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="c2">R2</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="c4">D'</font> &amp; <font color="Maroon" title="c5">x2</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">y2</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>reconsider </b><font color="Maroon" title="c7">x1</font> = <font color="Maroon" title="c5">x2</font>, <font color="Maroon" title="c8">y1</font> = <font color="Maroon" title="c6">y2</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R1</font> <b>by </b><i><a class="txt" href="waybel11.html#E1:85"><i><font color="Green" title="E55">A1</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon" title="c9">z1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R1</font><b> such that </b><br/><a NAME="E7:85"/><i><font color="Green" title="E59">A5</font></i>: 
<font color="Maroon" title="c9">z1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">D</font>
 <b>and </b><br/><a NAME="E8:85"/><i><font color="Green" title="E60">A6</font></i>: 
( <font color="Maroon" title="c7">x1</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c9">z1</font> &amp; <font color="Maroon" title="c8">y1</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c9">z1</font> )
 <b>by </b><i><a class="txt" href="waybel11.html#E2:85"><i><font color="Green" title="E56">A2</font></i></a>, <a class="txt" href="waybel11.html#E3:85"><i><font color="Green" title="E57">A3</font></i></a>, <a class="txt" href="waybel11.html#E4:85"><i><font color="Green" title="E58">A4</font></i></a>, <a class="ref" href="waybel_0.html#D1" title="WAYBEL_0:def.1">WAYBEL_0:def 1</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c10">z2</font> = <font color="Maroon" title="c9">z1</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">R2</font> <b>by </b><i><a class="txt" href="waybel11.html#E1:85"><i><font color="Green" title="E55">A1</font></i></a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c10">z2</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c10">z2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">D'</font> &amp; <font color="Maroon" title="c5">x2</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c10">z2</font> &amp; <font color="Maroon" title="c6">y2</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c10">z2</font> )</span><br/>

<b>thus </b><a NAME="E10:85"/>
<font color="Maroon" title="c10">z2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">D'</font>
 <b>by </b><i><a class="txt" href="waybel11.html#E2:85"><i><font color="Green" title="E56">A2</font></i></a>, <a class="txt" href="waybel11.html#E7:85"><i><font color="Green" title="E59">A5</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">x2</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c10">z2</font> &amp; <font color="Maroon" title="c6">y2</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c10">z2</font> )</span><br/>

<b>thus </b><a NAME="E11:85"/>
( <font color="Maroon" title="c5">x2</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c10">z2</font> &amp; <font color="Maroon" title="c6">y2</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c10">z2</font> )
 <b>by </b><i><a class="txt" href="waybel11.html#E1:85"><i><font color="Green" title="E55">A1</font></i></a>, <a class="txt" href="waybel11.html#E8:85"><i><font color="Green" title="E60">A6</font></i></a>, <a class="txt" href="waybel11.html#E1"><i><font color="Green" title="E1">Lm1</font></i></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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