<?xml version="1.0"?>
<div class="add">

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1">set</a> ,   <a href="hidden.html#M1">set</a> ] <b>means </b> ex <font color="Olive">y</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> st <br/>( <font color="Olive">y</font> <a href="hidden.html#R1">=</a> the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">N</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">a<sub>1</sub></font> &amp; <font color="Maroon">a<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> <a href="lattice3.html#K11">"/\"</a> <font color="Olive">y</font> );<br/>
<a NAME="E1:32_1_1"/><i><font color="Green">E29</font></i>: 
for <font color="Olive">e</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">N</font>  ex <font color="Olive">u</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">e</font>,<font color="Olive">u</font>]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="32_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">e</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">N</font>;<br/>

<b>take </b>
<font color="Maroon">x</font> <a href="lattice3.html#K11">"/\"</a> <span class="p1">(<span class="default">the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">N</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">e</font></span>)</span>
;<br/>

<b>take </b>
the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">N</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">e</font>
;<br/>

<b>thus </b><a NAME="E1:32_1_1_1"/>
( the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">N</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">N</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> &amp; <font color="Maroon">x</font> <a href="lattice3.html#K11">"/\"</a> <span class="p1">(<span class="default">the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">N</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">e</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> <a href="lattice3.html#K11">"/\"</a> <span class="p1">(<span class="default">the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">N</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">e</font></span>)</span> )
 ;<br/>


</div><b>end;</b></div>
<a NAME="E2:32_1_1"/>
 ex <font color="Olive">g</font> being  <a href="funct_2.html#NM1">Function</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">N</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font> st <br/>for <font color="Olive">i</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">N</font> holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">i</font>,<font color="Olive">g</font> <a href="funct_2.html#K3">.</a> <font color="Olive">i</font>]
 
<b>from </b><i><a class="ref" href="funct_2.html#S3">FUNCT_2:sch 3</a>();<br/></i>
<b>then consider </b><font color="Maroon">g</font> being   <a href="funct_2.html#NM1">Function</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">N</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E4:32_1_1"/><i><font color="Green">E32</font></i>: 
for <font color="Olive">i</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">N</font>  ex <font color="Olive">y</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> st <br/>( <font color="Olive">y</font> <a href="hidden.html#R1">=</a> the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">N</font> <a href="funct_2.html#K3">.</a> <font color="Olive">i</font> &amp; <font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> <a href="lattice3.html#K11">"/\"</a> <font color="Olive">y</font> )
 ;<br/>
<b>take </b>
 <a href="waybel_0.html#G1">NetStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">N</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">N</font>,<font color="Maroon">g</font> #)
;<br/>

<b>thus </b><a NAME="E5:32_1_1"/>
(  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <a href="waybel_0.html#G1">NetStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">N</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">N</font>,<font color="Maroon">g</font> #),the <a href="orders_2.html#U1">InternalRel</a> of <a href="waybel_0.html#G1">NetStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">N</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">N</font>,<font color="Maroon">g</font> #) #) <a href="hidden.html#R1">=</a>  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">N</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">N</font> #) &amp; ( for <font color="Olive">i</font> being  <a href="struct_0.html#NM1">Element</a> of <a href="waybel_0.html#G1">NetStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">N</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">N</font>,<font color="Maroon">g</font> #)  ex <font color="Olive">y</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> st <br/>( <font color="Olive">y</font> <a href="hidden.html#R1">=</a> the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">N</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> &amp; the <a href="waybel_0.html#U1">mapping</a> of <a href="waybel_0.html#G1">NetStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">N</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">N</font>,<font color="Maroon">g</font> #) <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> <a href="lattice3.html#K11">"/\"</a> <font color="Olive">y</font> ) ) )
 <b>by </b><i/>;<br/>


</div>
