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

<b>let </b><font color="Maroon" title="c1">L</font> be   <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">LATTICE</a>;<br/><b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>;<br/>



<b>assume </b><a NAME="E1:28"/><i><font color="Green" title="E16">A1</font></i>: 
<font color="Maroon" title="c1">L</font> is <a href="yellow11.html#V1" title="YELLOW11:attr.1">modular</a>
 ;<br/>

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ,   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ] <b>means </b>( $2 is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> &amp; ( 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">L</font>  st $1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">X</font> &amp; $2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">Y</font> holds <br/><font color="Olive" title="b2">Y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">X</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c2">a</font> ) );<br/>
<a NAME="E2:28"/><i><font color="Green" title="E17">A2</font></i>: 
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   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 <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <span class="p2"><a href="yellow11.html#K3" title="YELLOW11:func.3">[#</a><span class="default"><font color="Maroon" title="c3">b</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c3">b</font></span>)</span></span><a href="yellow11.html#K3" title="YELLOW11:func.3">#]</a></span></span>)</span> holds <br/> ex <font color="Olive" title="b2">y</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <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 <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <span class="p2"><a href="yellow11.html#K3" title="YELLOW11:func.3">[#</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c3">b</font></span>)</span>,<font color="Maroon" title="c2">a</font></span><a href="yellow11.html#K3" title="YELLOW11:func.3">#]</a></span></span>)</span> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>] )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c4">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E1:28_1"/>
<font color="Maroon" title="c4">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 <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <span class="p2"><a href="yellow11.html#K3" title="YELLOW11:func.3">[#</a><span class="default"><font color="Maroon" title="c3">b</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c3">b</font></span>)</span></span><a href="yellow11.html#K3" title="YELLOW11:func.3">#]</a></span></span>)</span>
 ;<br/>

<a NAME="E2:28_1"/><b>then </b><i><font color="Green" title="E18">A3</font></i>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="yellow11.html#K3" title="YELLOW11:func.3">[#</a><span class="default"><font color="Maroon" title="c3">b</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c3">b</font></span>)</span></span><a href="yellow11.html#K3" title="YELLOW11:func.3">#]</a></span>
 
<b>by </b><i><a class="ref" href="yellow_0.html#D15" title="YELLOW_0:def.15">YELLOW_0:def 15</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c5">x1</font> = <font color="Maroon" title="c4">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> ;<br/>
<b>take </b><font color="Maroon" title="c6">y</font> = <font color="Maroon" title="c2">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c5">x1</font>;<br/>

<a NAME="E4:28_1"/>
( <font color="Maroon" title="c3">b</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">x1</font> &amp; <font color="Maroon" title="c5">x1</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c2">a</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c3">b</font> )
 
<b>by </b><i><a class="txt" href="yellow11.html#E2:28_1"><i><font color="Green" title="E18">A3</font></i></a>, <a class="ref" href="yellow11.html#D4" target="_self" title="YELLOW11:def.4">Def4</a></i>;<br/>
<a NAME="E5:28_1"/><b>then </b>
( <font color="Maroon" title="c2">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c3">b</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c6">y</font> &amp; <font color="Maroon" title="c6">y</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c2">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c3">b</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="yellow_5.html#T6" title="YELLOW_5:th.6">YELLOW_5:6</a></i>;<br/>
<a NAME="E6:28_1"/><b>then </b>
( <font color="Maroon" title="c2">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c3">b</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c6">y</font> &amp; <font color="Maroon" title="c6">y</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c2">a</font> )
 
<b>by </b><i><a class="ref" href="lattice3.html#T18" title="LATTICE3:th.18">LATTICE3:18</a></i>;<br/>
<a NAME="E7:28_1"/><b>then </b>
<font color="Maroon" title="c6">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="yellow11.html#K3" title="YELLOW11:func.3">[#</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c3">b</font></span>)</span>,<font color="Maroon" title="c2">a</font></span><a href="yellow11.html#K3" title="YELLOW11:func.3">#]</a></span>
 
<b>by </b><i><a class="ref" href="yellow11.html#D4" target="_self" title="YELLOW11:def.4">Def4</a></i>;<br/>
<b>hence </b><a NAME="E8:28_1"/>
<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 <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <span class="p2"><a href="yellow11.html#K3" title="YELLOW11:func.3">[#</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c3">b</font></span>)</span>,<font color="Maroon" title="c2">a</font></span><a href="yellow11.html#K3" title="YELLOW11:func.3">#]</a></span></span>)</span>
 <b>by </b><i><a class="ref" href="yellow_0.html#D15" title="YELLOW_0:def.15">YELLOW_0:def 15</a></i>;<br/>

<b>thus </b><a NAME="E9:28_1"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c6">y</font>]
 ;<br/>


</div><b>end;</b></div>
<b>consider </b><font color="Maroon" title="c4">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of 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> <span class="p2"><a href="yellow11.html#K3" title="YELLOW11:func.3">[#</a><span class="default"><font color="Maroon" title="c3">b</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c3">b</font></span>)</span></span><a href="yellow11.html#K3" title="YELLOW11:func.3">#]</a></span></span>)</span>,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> <span class="p2"><a href="yellow11.html#K3" title="YELLOW11:func.3">[#</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c3">b</font></span>)</span>,<font color="Maroon" title="c2">a</font></span><a href="yellow11.html#K3" title="YELLOW11:func.3">#]</a></span></span>)</span><b> such that </b><br/><a NAME="E4:28"/><i><font color="Green" title="E18">A4</font></i>: 
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   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 <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <span class="p2"><a href="yellow11.html#K3" title="YELLOW11:func.3">[#</a><span class="default"><font color="Maroon" title="c3">b</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c3">b</font></span>)</span></span><a href="yellow11.html#K3" title="YELLOW11:func.3">#]</a></span></span>)</span> holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">x</font>,<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font>]
 <b>from </b><i><a class="ref" href="funct_2.html#S1" title="FUNCT_2:sch.1">FUNCT_2:sch 1</a>(<a class="txt" href="yellow11.html#E2:28"><i><font color="Green" title="E17">A2</font></i></a>);<br/></i>
<b>reconsider </b><font color="Maroon" title="c5">f</font> = <font color="Maroon" title="c4">f</font> as   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <span class="p2"><a href="yellow11.html#K3" title="YELLOW11:func.3">[#</a><span class="default"><font color="Maroon" title="c3">b</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c3">b</font></span>)</span></span><a href="yellow11.html#K3" title="YELLOW11:func.3">#]</a></span></span>)</span>,<span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <span class="p2"><a href="yellow11.html#K3" title="YELLOW11:func.3">[#</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c3">b</font></span>)</span>,<font color="Maroon" title="c2">a</font></span><a href="yellow11.html#K3" title="YELLOW11:func.3">#]</a></span></span>)</span> ;<br/>
<b>take </b>
<font color="Maroon" title="c5">f</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_1.html#D8" title="WAYBEL_1:def.8">WAYBEL_1:def 8</a><br/>

<b>thus </b><a NAME="E6:28"/>
<font color="Maroon" title="c5">f</font> is <a href="waybel_0.html#V23" title="WAYBEL_0:attr.23">isomorphic</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_2"><b>proof </b></a><div class="add">

<a NAME="E1:28_2"/>
not  <a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <span class="p1"><a href="yellow11.html#K3" title="YELLOW11:func.3">[#</a><span class="default"><font color="Maroon" title="c3">b</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c2">a</font></span>)</span></span><a href="yellow11.html#K3" title="YELLOW11:func.3">#]</a></span> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_2_1"><b>proof </b></a><div class="add">

<a NAME="E1:28_2_1"/>
( <font color="Maroon" title="c3">b</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c3">b</font> &amp; <font color="Maroon" title="c3">b</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c2">a</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c3">b</font> )
 
<b>by </b><i><a class="ref" href="yellow_0.html#T22" title="YELLOW_0:th.22">YELLOW_0:22</a></i>;<br/>
<a NAME="E2:28_2_1"/><b>then </b>
<font color="Maroon" title="c3">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="yellow11.html#K3" title="YELLOW11:func.3">[#</a><span class="default"><font color="Maroon" title="c3">b</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c3">b</font></span>)</span></span><a href="yellow11.html#K3" title="YELLOW11:func.3">#]</a></span>
 
<b>by </b><i><a class="ref" href="yellow11.html#D4" target="_self" title="YELLOW11:def.4">Def4</a></i>;<br/>
<a NAME="E3:28_2_1"/><b>then </b>
<font color="Maroon" title="c3">b</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 <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <span class="p2"><a href="yellow11.html#K3" title="YELLOW11:func.3">[#</a><span class="default"><font color="Maroon" title="c3">b</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c3">b</font></span>)</span></span><a href="yellow11.html#K3" title="YELLOW11:func.3">#]</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="yellow_0.html#D15" title="YELLOW_0:def.15">YELLOW_0:def 15</a></i>;<br/>
<b>hence </b><a NAME="E4:28_2_1"/>
not  <a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <span class="p1"><a href="yellow11.html#K3" title="YELLOW11:func.3">[#</a><span class="default"><font color="Maroon" title="c3">b</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c2">a</font></span>)</span></span><a href="yellow11.html#K3" title="YELLOW11:func.3">#]</a></span> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>
 <b>by </b><i><a class="ref" href="struct_0.html#D1" title="STRUCT_0:def.1">STRUCT_0:def 1</a></i>;<br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon" title="c6">s1</font> =  <a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <span class="p1"><a href="yellow11.html#K3" title="YELLOW11:func.3">[#</a><span class="default"><font color="Maroon" title="c3">b</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c2">a</font></span>)</span></span><a href="yellow11.html#K3" title="YELLOW11:func.3">#]</a></span> as  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="yellow_0.html#V4" title="YELLOW_0:attr.4">full</a> <a href="lattice5.html#NM2" title="LATTICE5:NM.2">Sublattice</a> of <font color="Maroon" title="c1">L</font> ;<br/>
<a NAME="E3:28_2"/>
not  <a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <span class="p1"><a href="yellow11.html#K3" title="YELLOW11:func.3">[#</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c3">b</font></span>)</span>,<font color="Maroon" title="c2">a</font></span><a href="yellow11.html#K3" title="YELLOW11:func.3">#]</a></span> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_2_2"><b>proof </b></a><div class="add">

<a NAME="E1:28_2_2"/>
( <font color="Maroon" title="c2">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c3">b</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c2">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c3">b</font> &amp; <font color="Maroon" title="c2">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c3">b</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c2">a</font> )
 
<b>by </b><i><a class="ref" href="yellow_0.html#T23" title="YELLOW_0:th.23">YELLOW_0:23</a></i>;<br/>
<a NAME="E2:28_2_2"/><b>then </b>
<font color="Maroon" title="c2">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c3">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="yellow11.html#K3" title="YELLOW11:func.3">[#</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c3">b</font></span>)</span>,<font color="Maroon" title="c2">a</font></span><a href="yellow11.html#K3" title="YELLOW11:func.3">#]</a></span>
 
<b>by </b><i><a class="ref" href="yellow11.html#D4" target="_self" title="YELLOW11:def.4">Def4</a></i>;<br/>
<a NAME="E3:28_2_2"/><b>then </b>
<font color="Maroon" title="c2">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c3">b</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 <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <span class="p2"><a href="yellow11.html#K3" title="YELLOW11:func.3">[#</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c3">b</font></span>)</span>,<font color="Maroon" title="c2">a</font></span><a href="yellow11.html#K3" title="YELLOW11:func.3">#]</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="yellow_0.html#D15" title="YELLOW_0:def.15">YELLOW_0:def 15</a></i>;<br/>
<b>hence </b><a NAME="E4:28_2_2"/>
not  <a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <span class="p1"><a href="yellow11.html#K3" title="YELLOW11:func.3">[#</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c3">b</font></span>)</span>,<font color="Maroon" title="c2">a</font></span><a href="yellow11.html#K3" title="YELLOW11:func.3">#]</a></span> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>
 <b>by </b><i><a class="ref" href="struct_0.html#D1" title="STRUCT_0:def.1">STRUCT_0:def 1</a></i>;<br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon" title="c7">s2</font> =  <a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <span class="p1"><a href="yellow11.html#K3" title="YELLOW11:func.3">[#</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c3">b</font></span>)</span>,<font color="Maroon" title="c2">a</font></span><a href="yellow11.html#K3" title="YELLOW11:func.3">#]</a></span> as  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="yellow_0.html#V4" title="YELLOW_0:attr.4">full</a> <a href="lattice5.html#NM2" title="LATTICE5:NM.2">Sublattice</a> of <font color="Maroon" title="c1">L</font> ;<br/>
<b>reconsider </b><font color="Maroon" title="c8">f1</font> = <font color="Maroon" title="c5">f</font> as   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c6">s1</font>,<font color="Maroon" title="c7">s2</font> ;<br/>
<a NAME="E6:28_2"/>
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c8">f1</font> <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> <span class="p2"><a href="yellow11.html#K3" title="YELLOW11:func.3">[#</a><span class="default"><font color="Maroon" title="c3">b</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c3">b</font></span>)</span></span><a href="yellow11.html#K3" title="YELLOW11:func.3">#]</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E7:28_2"/><b>then </b><i><font color="Green" title="E19">A5</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c8">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="yellow11.html#K3" title="YELLOW11:func.3">[#</a><span class="default"><font color="Maroon" title="c3">b</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c3">b</font></span>)</span></span><a href="yellow11.html#K3" title="YELLOW11:func.3">#]</a></span>
 
<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="E8:28_2"/><i><font color="Green" title="E20">A6</font></i>: 
<font color="Maroon" title="c8">f1</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_2_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c9">x1</font>, <font color="Maroon" title="c10">x2</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="funct_1.html#D8" title="FUNCT_1:def.8">FUNCT_1:def 8</a><br/>

<b>assume </b><a NAME="E1:28_2_3"/><i><font color="Green" title="E21">A7</font></i>: 
( <font color="Maroon" title="c9">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c8">f1</font> &amp; <font color="Maroon" title="c10">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c8">f1</font> &amp; <font color="Maroon" title="c8">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x2</font> )
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c11">X1</font> = <font color="Maroon" title="c9">x1</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> <b>by </b><i><a class="txt" href="yellow11.html#E7:28_2"><i><font color="Green" title="E19">A5</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c12">X2</font> = <font color="Maroon" title="c10">x2</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> <b>by </b><i><a class="txt" href="yellow11.html#E7:28_2"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="yellow11.html#E1:28_2_3"><i><font color="Green" title="E21">A7</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c13">f1X1</font> = <font color="Maroon" title="c8">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">X1</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> <b>by </b><i><a class="txt" href="yellow11.html#E4:28"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="yellow11.html#E1:28_2_3"><i><font color="Green" title="E21">A7</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c14">f1X2</font> = <font color="Maroon" title="c8">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">X2</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> <b>by </b><i><a class="txt" href="yellow11.html#E4:28"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="yellow11.html#E1:28_2_3"><i><font color="Green" title="E21">A7</font></i></a></i>;<br/>
<a NAME="E6:28_2_3"/><i><font color="Green" title="E22">A8</font></i>: 
( <font color="Maroon" title="c3">b</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c11">X1</font> &amp; <font color="Maroon" title="c11">X1</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c2">a</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c3">b</font> &amp; <font color="Maroon" title="c3">b</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c12">X2</font> &amp; <font color="Maroon" title="c12">X2</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c2">a</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c3">b</font> )
 
<b>by </b><i><a class="txt" href="yellow11.html#E7:28_2"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="yellow11.html#E1:28_2_3"><i><font color="Green" title="E21">A7</font></i></a>, <a class="ref" href="yellow11.html#D4" target="_self" title="YELLOW11:def.4">Def4</a></i>;<br/>
<a NAME="E7:28_2_3"/><i><font color="Green" title="E23">A9</font></i>: 
( <font color="Maroon" title="c13">f1X1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">X1</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c2">a</font> &amp; <font color="Maroon" title="c14">f1X2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">X2</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c2">a</font> )
 
<b>by </b><i><a class="txt" href="yellow11.html#E4:28"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="yellow11.html#E1:28_2_3"><i><font color="Green" title="E21">A7</font></i></a></i>;<br/>
<font color="Maroon" title="c11">X1</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c11">X1</font>
<b>by </b><i><a class="txt" href="yellow11.html#E6:28_2_3"><i><font color="Green" title="E22">A8</font></i></a>, <a class="ref" href="yellow_5.html#T10" title="YELLOW_5:th.10">YELLOW_5:10</a></i>
<br/>.= 
<font color="Maroon" title="c3">b</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c12">X2</font></span>)</span>
<b>by </b><i><a class="txt" href="yellow11.html#E1:28"><i><font color="Green" title="E16">A1</font></i></a>, <a class="txt" href="yellow11.html#E1:28_2_3"><i><font color="Green" title="E21">A7</font></i></a>, <a class="txt" href="yellow11.html#E6:28_2_3"><i><font color="Green" title="E22">A8</font></i></a>, <a class="txt" href="yellow11.html#E7:28_2_3"><i><font color="Green" title="E23">A9</font></i></a>, <a class="ref" href="yellow11.html#D3" target="_self" title="YELLOW11:def.3">Def3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c12">X2</font>
<b>by </b><i><a class="txt" href="yellow11.html#E1:28"><i><font color="Green" title="E16">A1</font></i></a>, <a class="txt" href="yellow11.html#E6:28_2_3"><i><font color="Green" title="E22">A8</font></i></a>, <a class="ref" href="yellow11.html#D3" target="_self" title="YELLOW11:def.3">Def3</a></i>
<br/>.= 
<font color="Maroon" title="c12">X2</font>
<b>by </b><i><a class="txt" href="yellow11.html#E6:28_2_3"><i><font color="Green" title="E22">A8</font></i></a>, <a class="ref" href="yellow_5.html#T10" title="YELLOW_5:th.10">YELLOW_5:10</a></i>
;<br/>
<b>hence </b><a NAME="E9:28_2_3"/>
<font color="Maroon" title="c9">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">x2</font>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E9:28_2"/><i><font color="Green" title="E21">A10</font></i>: 
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c8">f1</font> <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> <span class="p2"><a href="yellow11.html#K3" title="YELLOW11:func.3">[#</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c3">b</font></span>)</span>,<font color="Maroon" title="c2">a</font></span><a href="yellow11.html#K3" title="YELLOW11:func.3">#]</a></span></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_2_4"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:28_2_4"/>
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c8">f1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</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> <span class="p2"><a href="yellow11.html#K3" title="YELLOW11:func.3">[#</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c3">b</font></span>)</span>,<font color="Maroon" title="c2">a</font></span><a href="yellow11.html#K3" title="YELLOW11:func.3">#]</a></span></span>)</span>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a><br/>

<b>thus </b><a NAME="E2:28_2_4"/>
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> <span class="p2"><a href="yellow11.html#K3" title="YELLOW11:func.3">[#</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c3">b</font></span>)</span>,<font color="Maroon" title="c2">a</font></span><a href="yellow11.html#K3" title="YELLOW11:func.3">#]</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c8">f1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_2_4_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c9">y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:28_2_4_1"/>
<font color="Maroon" title="c9">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 <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <span class="p2"><a href="yellow11.html#K3" title="YELLOW11:func.3">[#</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c3">b</font></span>)</span>,<font color="Maroon" title="c2">a</font></span><a href="yellow11.html#K3" title="YELLOW11:func.3">#]</a></span></span>)</span>
 ;<br/>

<a NAME="E2:28_2_4_1"/><b>then </b><i><font color="Green" title="E22">A11</font></i>: 
<font color="Maroon" title="c9">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="yellow11.html#K3" title="YELLOW11:func.3">[#</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c3">b</font></span>)</span>,<font color="Maroon" title="c2">a</font></span><a href="yellow11.html#K3" title="YELLOW11:func.3">#]</a></span>
 
<b>by </b><i><a class="ref" href="yellow_0.html#D15" title="YELLOW_0:def.15">YELLOW_0:def 15</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c10">Y</font> = <font color="Maroon" title="c9">y</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> ;<br/>
<a NAME="E4:28_2_4_1"/><i><font color="Green" title="E23">A12</font></i>: 
( <font color="Maroon" title="c2">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c3">b</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c10">Y</font> &amp; <font color="Maroon" title="c10">Y</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c2">a</font> )
 
<b>by </b><i><a class="txt" href="yellow11.html#E2:28_2_4_1"><i><font color="Green" title="E22">A11</font></i></a>, <a class="ref" href="yellow11.html#D4" target="_self" title="YELLOW11:def.4">Def4</a></i>;<br/>
<a NAME="E5:28_2_4_1"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c3">b</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c10">Y</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c3">b</font> &amp; <font color="Maroon" title="c10">Y</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c3">b</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c2">a</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c3">b</font> )
 
<b>by </b><i><a class="ref" href="waybel_1.html#T3" title="WAYBEL_1:th.3">WAYBEL_1:3</a></i>;<br/>
<a NAME="E6:28_2_4_1"/><b>then </b>
( <font color="Maroon" title="c3">b</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c10">Y</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c3">b</font> &amp; <font color="Maroon" title="c10">Y</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c3">b</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c2">a</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c3">b</font> )
 
<b>by </b><i><a class="ref" href="lattice3.html#T17" title="LATTICE3:th.17">LATTICE3:17</a></i>;<br/>
<a NAME="E7:28_2_4_1"/><b>then </b><i><font color="Green" title="E24">A13</font></i>: 
<font color="Maroon" title="c10">Y</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c3">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="yellow11.html#K3" title="YELLOW11:func.3">[#</a><span class="default"><font color="Maroon" title="c3">b</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c3">b</font></span>)</span></span><a href="yellow11.html#K3" title="YELLOW11:func.3">#]</a></span>
 
<b>by </b><i><a class="ref" href="yellow11.html#D4" target="_self" title="YELLOW11:def.4">Def4</a></i>;<br/>
<a NAME="E8:28_2_4_1"/><b>then </b><i><font color="Green" title="E25">A14</font></i>: 
<font color="Maroon" title="c10">Y</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c3">b</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 <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <span class="p2"><a href="yellow11.html#K3" title="YELLOW11:func.3">[#</a><span class="default"><font color="Maroon" title="c3">b</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c3">b</font></span>)</span></span><a href="yellow11.html#K3" title="YELLOW11:func.3">#]</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="yellow_0.html#D15" title="YELLOW_0:def.15">YELLOW_0:def 15</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c11">f1yb</font> = <font color="Maroon" title="c8">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">Y</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c3">b</font></span>)</span> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> <b>by </b><i><a class="txt" href="yellow11.html#E4:28"><i><font color="Green" title="E18">A4</font></i></a></i>;<br/>
<font color="Maroon" title="c11">f1yb</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c10">Y</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c2">a</font>
<b>by </b><i><a class="txt" href="yellow11.html#E4:28"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="yellow11.html#E8:28_2_4_1"><i><font color="Green" title="E25">A14</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c10">Y</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c2">a</font></span>)</span>
<b>by </b><i><a class="txt" href="yellow11.html#E1:28"><i><font color="Green" title="E16">A1</font></i></a>, <a class="txt" href="yellow11.html#E4:28_2_4_1"><i><font color="Green" title="E23">A12</font></i></a>, <a class="ref" href="yellow11.html#D3" target="_self" title="YELLOW11:def.3">Def3</a></i>
<br/>.= 
<font color="Maroon" title="c10">Y</font>
<b>by </b><i><a class="txt" href="yellow11.html#E4:28_2_4_1"><i><font color="Green" title="E23">A12</font></i></a>, <a class="ref" href="yellow_5.html#T8" title="YELLOW_5:th.8">YELLOW_5:8</a></i>
;<br/>
<b>hence </b><a NAME="E11:28_2_4_1"/>
<font color="Maroon" title="c9">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c8">f1</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E7:28_2"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="yellow11.html#E7:28_2_4_1"><i><font color="Green" title="E24">A13</font></i></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>


</div><b>end;</b></div>


</div><b>end;</b></div>
<a NAME="E10:28_2"/>
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="c6">s1</font> holds <br/> ( <font color="Olive" title="b1">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Olive" title="b2">y</font> iff <font color="Maroon" title="c8">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c8">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">y</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_2_5"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c9">x</font>, <font color="Maroon" title="c10">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c6">s1</font>;<br/>

<a NAME="E1:28_2_5"/><i><font color="Green" title="E22">A15</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c6">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="yellow11.html#K3" title="YELLOW11:func.3">[#</a><span class="default"><font color="Maroon" title="c3">b</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c3">b</font></span>)</span></span><a href="yellow11.html#K3" title="YELLOW11:func.3">#]</a></span>
 
<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="E2:28_2_5"/><b>then </b><i><font color="Green" title="E23">A16</font></i>: 
( <font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="yellow11.html#K3" title="YELLOW11:func.3">[#</a><span class="default"><font color="Maroon" title="c3">b</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c3">b</font></span>)</span></span><a href="yellow11.html#K3" title="YELLOW11:func.3">#]</a></span> &amp; <font color="Maroon" title="c10">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="yellow11.html#K3" title="YELLOW11:func.3">[#</a><span class="default"><font color="Maroon" title="c3">b</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c3">b</font></span>)</span></span><a href="yellow11.html#K3" title="YELLOW11:func.3">#]</a></span> )
 
;<br/>
<b>then reconsider </b><font color="Maroon" title="c11">X</font> = <font color="Maroon" title="c9">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> ;<br/>
<b>reconsider </b><font color="Maroon" title="c12">Y</font> = <font color="Maroon" title="c10">y</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> <b>by </b><i><a class="txt" href="yellow11.html#E2:28_2_5"><i><font color="Green" title="E23">A16</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c13">f1X</font> = <font color="Maroon" title="c8">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">X</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> <b>by </b><i><a class="txt" href="yellow11.html#E4:28"><i><font color="Green" title="E18">A4</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c14">f1Y</font> = <font color="Maroon" title="c8">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">Y</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> <b>by </b><i><a class="txt" href="yellow11.html#E4:28"><i><font color="Green" title="E18">A4</font></i></a></i>;<br/>
<b>thus </b><a NAME="E7:28_2_5"/>
( <font color="Maroon" title="c9">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c10">y</font> implies <font color="Maroon" title="c8">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c8">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">y</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_2_5_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:28_2_5_1"/>
<font color="Maroon" title="c9">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c10">y</font>
 ;<br/>

<a NAME="E2:28_2_5_1"/><b>then </b><i><font color="Green" title="E24">A17</font></i>: 
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c9">x</font>,<font color="Maroon" title="c10">y</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c6">s1</font>
 
<b>by </b><i><a class="ref" href="orders_2.html#D9" title="ORDERS_2:def.9">ORDERS_2:def 9</a></i>;<br/>
<a NAME="E3:28_2_5_1"/>
the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c6">s1</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">L</font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#D13" title="YELLOW_0:def.13">YELLOW_0:def 13</a></i>;<br/>
<a NAME="E4:28_2_5_1"/><b>then </b><i><font color="Green" title="E25">A18</font></i>: 
<font color="Maroon" title="c11">X</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c12">Y</font>
 
<b>by </b><i><a class="txt" href="yellow11.html#E2:28_2_5_1"><i><font color="Green" title="E24">A17</font></i></a>, <a class="ref" href="orders_2.html#D9" title="ORDERS_2:def.9">ORDERS_2:def 9</a></i>;<br/>
<a NAME="E5:28_2_5_1"/>
( <font color="Maroon" title="c13">f1X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">X</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c2">a</font> &amp; <font color="Maroon" title="c14">f1Y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">Y</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c2">a</font> )
 
<b>by </b><i><a class="txt" href="yellow11.html#E4:28"><i><font color="Green" title="E18">A4</font></i></a></i>;<br/>
<a NAME="E6:28_2_5_1"/><b>then </b>
<font color="Maroon" title="c13">f1X</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c14">f1Y</font>
 
<b>by </b><i><a class="txt" href="yellow11.html#E4:28_2_5_1"><i><font color="Green" title="E25">A18</font></i></a>, <a class="ref" href="waybel_1.html#T2" title="WAYBEL_1:th.2">WAYBEL_1:2</a></i>;<br/>
<b>hence </b><a NAME="E7:28_2_5_1"/>
<font color="Maroon" title="c8">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c8">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">y</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T61" title="YELLOW_0:th.61">YELLOW_0:61</a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E8:28_2_5"/>
( <font color="Maroon" title="c8">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c8">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">y</font> implies <font color="Maroon" title="c9">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c10">y</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_2_5_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:28_2_5_2"/>
<font color="Maroon" title="c8">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c8">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">y</font>
 ;<br/>

<a NAME="E2:28_2_5_2"/><b>then </b><i><font color="Green" title="E24">A19</font></i>: 
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">x</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">y</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c7">s2</font>
 
<b>by </b><i><a class="ref" href="orders_2.html#D9" title="ORDERS_2:def.9">ORDERS_2:def 9</a></i>;<br/>
<a NAME="E3:28_2_5_2"/>
the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c7">s2</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">L</font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#D13" title="YELLOW_0:def.13">YELLOW_0:def 13</a></i>;<br/>
<a NAME="E4:28_2_5_2"/><b>then </b><i><font color="Green" title="E25">A20</font></i>: 
<font color="Maroon" title="c13">f1X</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c14">f1Y</font>
 
<b>by </b><i><a class="txt" href="yellow11.html#E2:28_2_5_2"><i><font color="Green" title="E24">A19</font></i></a>, <a class="ref" href="orders_2.html#D9" title="ORDERS_2:def.9">ORDERS_2:def 9</a></i>;<br/>
<a NAME="E5:28_2_5_2"/>
( <font color="Maroon" title="c13">f1X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">X</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c2">a</font> &amp; <font color="Maroon" title="c14">f1Y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">Y</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c2">a</font> )
 
<b>by </b><i><a class="txt" href="yellow11.html#E4:28"><i><font color="Green" title="E18">A4</font></i></a></i>;<br/>
<a NAME="E6:28_2_5_2"/><b>then </b><i><font color="Green" title="E26">A21</font></i>: 
<font color="Maroon" title="c3">b</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c11">X</font></span>)</span> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c3">b</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c12">Y</font></span>)</span>
 
<b>by </b><i><a class="txt" href="yellow11.html#E4:28_2_5_2"><i><font color="Green" title="E25">A20</font></i></a>, <a class="ref" href="waybel_1.html#T3" title="WAYBEL_1:th.3">WAYBEL_1:3</a></i>;<br/>
<a NAME="E7:28_2_5_2"/><i><font color="Green" title="E27">A22</font></i>: 
( <font color="Maroon" title="c3">b</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c11">X</font> &amp; <font color="Maroon" title="c11">X</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c3">b</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c2">a</font> &amp; <font color="Maroon" title="c3">b</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c12">Y</font> &amp; <font color="Maroon" title="c12">Y</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c3">b</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c2">a</font> )
 
<b>by </b><i><a class="txt" href="yellow11.html#E1:28_2_5"><i><font color="Green" title="E22">A15</font></i></a>, <a class="ref" href="yellow11.html#D4" target="_self" title="YELLOW11:def.4">Def4</a></i>;<br/>
<a NAME="E8:28_2_5_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c11">X</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c3">b</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c12">Y</font></span>)</span>
 
<b>by </b><i><a class="txt" href="yellow11.html#E1:28"><i><font color="Green" title="E16">A1</font></i></a>, <a class="txt" href="yellow11.html#E6:28_2_5_2"><i><font color="Green" title="E26">A21</font></i></a>, <a class="ref" href="yellow11.html#D3" target="_self" title="YELLOW11:def.3">Def3</a></i>;<br/>
<a NAME="E9:28_2_5_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c11">X</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c12">Y</font>
 
<b>by </b><i><a class="txt" href="yellow11.html#E1:28"><i><font color="Green" title="E16">A1</font></i></a>, <a class="txt" href="yellow11.html#E7:28_2_5_2"><i><font color="Green" title="E27">A22</font></i></a>, <a class="ref" href="yellow11.html#D3" target="_self" title="YELLOW11:def.3">Def3</a></i>;<br/>
<a NAME="E10:28_2_5_2"/><b>then </b>
<font color="Maroon" title="c11">X</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c12">Y</font>
 
<b>by </b><i><a class="txt" href="yellow11.html#E7:28_2_5_2"><i><font color="Green" title="E27">A22</font></i></a>, <a class="ref" href="yellow_5.html#T10" title="YELLOW_5:th.10">YELLOW_5:10</a></i>;<br/>
<a NAME="E11:28_2_5_2"/><b>then </b>
<font color="Maroon" title="c11">X</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c12">Y</font>
 
<b>by </b><i><a class="txt" href="yellow11.html#E7:28_2_5_2"><i><font color="Green" title="E27">A22</font></i></a>, <a class="ref" href="yellow_5.html#T10" title="YELLOW_5:th.10">YELLOW_5:10</a></i>;<br/>
<b>hence </b><a NAME="E12:28_2_5_2"/>
<font color="Maroon" title="c9">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c10">y</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T61" title="YELLOW_0:th.61">YELLOW_0:61</a></i>;<br/>


</div><b>end;</b></div>


</div><b>end;</b></div>
<b>hence </b><a NAME="E11:28_2"/>
<font color="Maroon" title="c5">f</font> is <a href="waybel_0.html#V23" title="WAYBEL_0:attr.23">isomorphic</a>
 <b>by </b><i><a class="txt" href="yellow11.html#E8:28_2"><i><font color="Green" title="E20">A6</font></i></a>, <a class="txt" href="yellow11.html#E9:28_2"><i><font color="Green" title="E21">A10</font></i></a>, <a class="ref" href="waybel_0.html#T66" title="WAYBEL_0:th.66">WAYBEL_0:66</a></i>;<br/>


</div><b>end;</b></div>


</div>
