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<b>let </b><font color="Maroon" title="c4">A</font>, <font color="Maroon" title="c5">B</font> be  <a href="waybel_0.html#V6" title="WAYBEL_0:attr.6">strict</a>  <a href="waybel_0.html#L1" title="WAYBEL_0:struct.1">NetStr</a> of <font color="Maroon" title="c1">L</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:32_1_2"/><i><font color="Green" title="E19">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 <font color="Maroon" title="c4">A</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c4">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="c3">N</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c3">N</font> #) &amp; ( for <font color="Olive" title="b1">i</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">A</font>  ex <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">L</font> st <br/>( <font color="Olive" title="b2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="waybel_0.html#U1" title="WAYBEL_0:sel.1">mapping</a> of <font color="Maroon" title="c3">N</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> &amp; the <a href="waybel_0.html#U1" title="WAYBEL_0:sel.1">mapping</a> of <font color="Maroon" title="c4">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> <a href="lattice3.html#K11" title="LATTICE3:func.11">"/\"</a> <font color="Olive" title="b2">y</font> ) ) )
 <b>and </b><br/><a NAME="E2:32_1_2"/><i><font color="Green" title="E20">A4</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="c5">B</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c5">B</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="c3">N</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c3">N</font> #) &amp; ( for <font color="Olive" title="b1">i</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c5">B</font>  ex <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">L</font> st <br/>( <font color="Olive" title="b2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="waybel_0.html#U1" title="WAYBEL_0:sel.1">mapping</a> of <font color="Maroon" title="c3">N</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> &amp; the <a href="waybel_0.html#U1" title="WAYBEL_0:sel.1">mapping</a> of <font color="Maroon" title="c5">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> <a href="lattice3.html#K11" title="LATTICE3:func.11">"/\"</a> <font color="Olive" title="b2">y</font> ) ) )
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c6">C</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">A</font> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  <b>by </b><i><a class="txt" href="waybel_2.html#E1:32_1_2"><i><font color="Green" title="E19">A3</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c7">f1</font> = the <a href="waybel_0.html#U1" title="WAYBEL_0:sel.1">mapping</a> of <font color="Maroon" title="c4">A</font>, <font color="Maroon" title="c8">f2</font> = the <a href="waybel_0.html#U1" title="WAYBEL_0:sel.1">mapping</a> of <font color="Maroon" title="c5">B</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c6">C</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font> <b>by </b><i><a class="txt" href="waybel_2.html#E1:32_1_2"><i><font color="Green" title="E19">A3</font></i></a>, <a class="txt" href="waybel_2.html#E2:32_1_2"><i><font color="Green" title="E20">A4</font></i></a></i>;<br/>
<a NAME="E5:32_1_2"/>
for <font color="Olive" title="b1">c</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c6">C</font> holds  <font color="Maroon" title="c7">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">f2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">c</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="32_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c9">c</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c6">C</font>;<br/>

<b>consider </b><font color="Maroon" title="c10">ya</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="E2:32_1_2_1"/><i><font color="Green" title="E21">A5</font></i>: 
( <font color="Maroon" title="c10">ya</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="waybel_0.html#U1" title="WAYBEL_0:sel.1">mapping</a> of <font color="Maroon" title="c3">N</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">c</font> &amp; <font color="Maroon" title="c7">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> <a href="lattice3.html#K11" title="LATTICE3:func.11">"/\"</a> <font color="Maroon" title="c10">ya</font> )
 <b>by </b><i><a class="txt" href="waybel_2.html#E1:32_1_2"><i><font color="Green" title="E19">A3</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon" title="c11">yb</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="E4:32_1_2_1"/><i><font color="Green" title="E22">A6</font></i>: 
( <font color="Maroon" title="c11">yb</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="waybel_0.html#U1" title="WAYBEL_0:sel.1">mapping</a> of <font color="Maroon" title="c3">N</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">c</font> &amp; <font color="Maroon" title="c8">f2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> <a href="lattice3.html#K11" title="LATTICE3:func.11">"/\"</a> <font color="Maroon" title="c11">yb</font> )
 <b>by </b><i><a class="txt" href="waybel_2.html#E1:32_1_2"><i><font color="Green" title="E19">A3</font></i></a>, <a class="txt" href="waybel_2.html#E2:32_1_2"><i><font color="Green" title="E20">A4</font></i></a></i>;<br/>
<b>thus </b><a NAME="E5:32_1_2_1"/>
<font color="Maroon" title="c7">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">f2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">c</font>
 <b>by </b><i><a class="txt" href="waybel_2.html#E2:32_1_2_1"><i><font color="Green" title="E21">A5</font></i></a>, <a class="txt" href="waybel_2.html#E4:32_1_2_1"><i><font color="Green" title="E22">A6</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E6:32_1_2"/>
<font color="Maroon" title="c4">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">B</font>
 <b>by </b><i><a class="txt" href="waybel_2.html#E1:32_1_2"><i><font color="Green" title="E19">A3</font></i></a>, <a class="txt" href="waybel_2.html#E2:32_1_2"><i><font color="Green" title="E20">A4</font></i></a>, <a class="ref" href="funct_2.html#T113" title="FUNCT_2:th.113">FUNCT_2:113</a></i>;<br/>


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