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<b>let </b><font color="Maroon" title="c1">L1</font>, <font color="Maroon" title="c2">L2</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a>  <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ;<br/><b>let </b><font color="Maroon" title="c3">A</font> be    <a href="yellow_0.html#M1" title="YELLOW_0:mode.1">SubRelStr</a> of <font color="Maroon" title="c1">L1</font>;<br/><b>let </b><font color="Maroon" title="c4">J</font> be    <a href="yellow_0.html#M1" title="YELLOW_0:mode.1">SubRelStr</a> of <font color="Maroon" title="c2">L2</font>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:20"/><i><font color="Green" title="E11">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">L1</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">L1</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">L2</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">L2</font> #) &amp;  <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="c3">A</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c3">A</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="c4">J</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c4">J</font> #) )
 <b>and </b><br/><a NAME="E2:20"/><i><font color="Green" title="E12">A2</font></i>: 
for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L1</font>  st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">A</font> &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">A</font> &amp;  <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L1</font> holds <br/> <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">A</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_0.html#D16" title="YELLOW_0:def.16">YELLOW_0:def 16</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 <font color="Maroon" title="c2">L2</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_0.html#D16" title="YELLOW_0:def.16">YELLOW_0:def 16</a><br/>

<b>assume </b><b>that </b><br/><a NAME="E3:20"/><i><font color="Green" title="E13">A3</font></i>: 
( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">J</font> &amp; <font color="Maroon" title="c6">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">J</font> )
 <b>and </b><br/><a NAME="E4:20"/><i><font color="Green" title="E14">A4</font></i>: 
 <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c2">L2</font>
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c7">x1</font> = <font color="Maroon" title="c5">x</font>, <font color="Maroon" title="c8">y1</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">L1</font> <b>by </b><i><a class="txt" href="yellow12.html#E1:20"><i><font color="Green" title="E11">A1</font></i></a></i>;<br/>
<a NAME="E6:20"/>
 <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c7">x1</font>,<font color="Maroon" title="c8">y1</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L1</font>
 
<b>by </b><i><a class="txt" href="yellow12.html#E1:20"><i><font color="Green" title="E11">A1</font></i></a>, <a class="txt" href="yellow12.html#E4:20"><i><font color="Green" title="E14">A4</font></i></a>, <a class="ref" href="yellow_0.html#T14" title="YELLOW_0:th.14">YELLOW_0:14</a></i>;<br/>
<a NAME="E7:20"/><b>then </b>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c7">x1</font>,<font color="Maroon" title="c8">y1</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">A</font>
 
<b>by </b><i><a class="txt" href="yellow12.html#E1:20"><i><font color="Green" title="E11">A1</font></i></a>, <a class="txt" href="yellow12.html#E2:20"><i><font color="Green" title="E12">A2</font></i></a>, <a class="txt" href="yellow12.html#E3:20"><i><font color="Green" title="E13">A3</font></i></a></i>;<br/>
<b>hence </b><a NAME="E8:20"/>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">J</font>
 <b>by </b><i><a class="txt" href="yellow12.html#E1:20"><i><font color="Green" title="E11">A1</font></i></a>, <a class="txt" href="yellow12.html#E4:20"><i><font color="Green" title="E14">A4</font></i></a>, <a class="ref" href="yellow_0.html#T27" title="YELLOW_0:th.27">YELLOW_0:27</a></i>;<br/>


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