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<b>set </b><font color="Maroon" title="c3">I</font> = <font color="Maroon" title="c2">F</font>;<br/>
<b>set </b><font color="Maroon" title="c4">A</font> = <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="waybel_9.html#K4" title="WAYBEL_9:func.4">opp+id</a> ;<br/>
<b>let </b><font color="Maroon" title="c5">x</font>, <font color="Maroon" title="c6">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="waybel_9.html#K4" title="WAYBEL_9:func.4">opp+id</a> </span>)</span>; <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="ref" href="waybel_0.html#D6" title="WAYBEL_0:def.6">WAYBEL_0:def 6</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">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="waybel_9.html#K4" title="WAYBEL_9:func.4">opp+id</a> </span>)</span> or  not <font color="Maroon" title="c6">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="waybel_9.html#K4" title="WAYBEL_9:func.4">opp+id</a> </span>)</span> 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 <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="waybel_9.html#K4" title="WAYBEL_9:func.4">opp+id</a> </span>)</span> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="waybel_9.html#K4" title="WAYBEL_9:func.4">opp+id</a> </span>)</span> &amp; <font color="Maroon" title="c5">x</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">y</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> ) )</span><br/>

<a NAME="E1:24_1_1"/><i><font color="Green" title="E6">A1</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">F</font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#D15" title="YELLOW_0:def.15">YELLOW_0:def 15</a></i>;<br/>
<a NAME="E2:24_1_1"/><i><font color="Green" title="E7">A2</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="waybel_9.html#K4" title="WAYBEL_9:func.4">opp+id</a> </span>)</span> <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 <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">F</font></span>)</span>
 
<b>by </b><i><a class="ref" href="waybel_9.html#D6" title="WAYBEL_9:def.6">WAYBEL_9:def 6</a></i>;<br/>
<b>assume </b><a NAME="E3:24_1_1"/>
( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="waybel_9.html#K4" title="WAYBEL_9:func.4">opp+id</a> </span>)</span> &amp; <font color="Maroon" title="c6">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="waybel_9.html#K4" title="WAYBEL_9:func.4">opp+id</a> </span>)</span> )
 ; <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 <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="waybel_9.html#K4" title="WAYBEL_9:func.4">opp+id</a> </span>)</span> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="waybel_9.html#K4" title="WAYBEL_9:func.4">opp+id</a> </span>)</span> &amp; <font color="Maroon" title="c5">x</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">y</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 reconsider </b><font color="Maroon" title="c7">a</font> = <font color="Maroon" title="c5">x</font>, <font color="Maroon" title="c8">b</font> = <font color="Maroon" title="c6">y</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font> <b>by </b><i><a class="txt" href="#E1:24_1_1"><i><font color="Green" title="E6">A1</font></i></a>, <a class="txt" href="#E2:24_1_1"><i><font color="Green" title="E7">A2</font></i></a></i>;<br/>
<a NAME="E5:24_1_1"/><i><font color="Green" title="E8">A3</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 <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="waybel_9.html#K4" title="WAYBEL_9:func.4">opp+id</a> </span>)</span>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="waybel_9.html#K4" title="WAYBEL_9:func.4">opp+id</a> </span>)</span> #) <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 <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a> </span>)</span>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a> </span>)</span> #)
 
<b>by </b><i><a class="ref" href="waybel_9.html#T11" title="WAYBEL_9:th.11">WAYBEL_9:11</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c9">c</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font><b> such that </b><br/><a NAME="E7:24_1_1"/><i><font color="Green" title="E9">A4</font></i>: 
( <font color="Maroon" title="c9">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">F</font> &amp; <font color="Maroon" title="c7">a</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c9">c</font> &amp; <font color="Maroon" title="c8">b</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c9">c</font> )
 <b>by </b><i><a class="txt" href="#E1:24_1_1"><i><font color="Green" title="E6">A1</font></i></a>, <a class="txt" href="#E2:24_1_1"><i><font color="Green" title="E7">A2</font></i></a>, <a class="ref" href="waybel_0.html#D2" title="WAYBEL_0:def.2">WAYBEL_0:def 2</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c10">a1</font> = <font color="Maroon" title="c5">x</font>, <font color="Maroon" title="c11">b1</font> = <font color="Maroon" title="c6">y</font>, <font color="Maroon" title="c12">c1</font> = <font color="Maroon" title="c9">c</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">F</font></span>)</span> <b>by </b><i><a class="txt" href="#E7:24_1_1"><i><font color="Green" title="E9">A4</font></i></a>, <a class="ref" href="waybel_9.html#D6" title="WAYBEL_9:def.6">WAYBEL_9:def 6</a>, <a class="ref" href="yellow_0.html#D15" title="YELLOW_0:def.15">YELLOW_0:def 15</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c13">z</font> = <font color="Maroon" title="c9">c</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="waybel_9.html#K4" title="WAYBEL_9:func.4">opp+id</a> </span>)</span> <b>by </b><i><a class="txt" href="#E2:24_1_1"><i><font color="Green" title="E7">A2</font></i></a>, <a class="txt" href="#E7:24_1_1"><i><font color="Green" title="E9">A4</font></i></a>, <a class="ref" href="yellow_0.html#D15" title="YELLOW_0:def.15">YELLOW_0:def 15</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c13">z</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c13">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="waybel_9.html#K4" title="WAYBEL_9:func.4">opp+id</a> </span>)</span> &amp; <font color="Maroon" title="c5">x</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c13">z</font> &amp; <font color="Maroon" title="c6">y</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c13">z</font> )</span><br/>

<a NAME="E10:24_1_1"/><i><font color="Green" title="E10">A5</font></i>: 
( <font color="Maroon" title="c10">a1</font> <a href="lattice3.html#K8" title="LATTICE3:func.8">~</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">a1</font> &amp; <font color="Maroon" title="c11">b1</font> <a href="lattice3.html#K8" title="LATTICE3:func.8">~</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">b1</font> &amp; <font color="Maroon" title="c12">c1</font> <a href="lattice3.html#K8" title="LATTICE3:func.8">~</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">c1</font> )
 
<b>by </b><i><a class="ref" href="lattice3.html#D6" title="LATTICE3:def.6">LATTICE3:def 6</a></i>;<br/>
<a NAME="E11:24_1_1"/>
( <font color="Maroon" title="c10">a1</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c12">c1</font> &amp; <font color="Maroon" title="c11">b1</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c12">c1</font> )
 
<b>by </b><i><a class="txt" href="#E7:24_1_1"><i><font color="Green" title="E9">A4</font></i></a>, <a class="ref" href="yellow_0.html#T61" title="YELLOW_0:th.61">YELLOW_0:61</a></i>;<br/>
<a NAME="E12:24_1_1"/><b>then </b>
( <font color="Maroon" title="c10">a1</font> <a href="lattice3.html#K8" title="LATTICE3:func.8">~</a>  <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c12">c1</font> <a href="lattice3.html#K8" title="LATTICE3:func.8">~</a>  &amp; <font color="Maroon" title="c11">b1</font> <a href="lattice3.html#K8" title="LATTICE3:func.8">~</a>  <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c12">c1</font> <a href="lattice3.html#K8" title="LATTICE3:func.8">~</a>  )
 
<b>by </b><i><a class="ref" href="lattice3.html#T9" title="LATTICE3:th.9">LATTICE3:9</a></i>;<br/>
<b>hence </b><a NAME="E13:24_1_1"/>
( <font color="Maroon" title="c13">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="waybel_9.html#K4" title="WAYBEL_9:func.4">opp+id</a> </span>)</span> &amp; <font color="Maroon" title="c5">x</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c13">z</font> &amp; <font color="Maroon" title="c6">y</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c13">z</font> )
 <b>by </b><i><a class="txt" href="#E5:24_1_1"><i><font color="Green" title="E8">A3</font></i></a>, <a class="txt" href="#E10:24_1_1"><i><font color="Green" title="E10">A5</font></i></a>, <a class="ref" href="yellow_0.html#T1" title="YELLOW_0:th.1">YELLOW_0:1</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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