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

<b>let </b><font color="Maroon" title="c1">S</font>, <font color="Maroon" title="c2">T</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ;<br/><b>let </b><font color="Maroon" title="c3">R</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="yellow_0.html#M1" title="YELLOW_0:mode.1">SubRelStr</a> of <font color="Maroon" title="c1">S</font>;<br/><b>let </b><font color="Maroon" title="c4">f</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">T</font>;<br/><b>let </b><font color="Maroon" title="c5">g</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c1">S</font>;<br/>







<b>assume </b><a NAME="E1:21"/><i><font color="Green" title="E9">A1</font></i>: 
( <font color="Maroon" title="c4">f</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a> &amp; <font color="Maroon" title="c5">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a>  )
 ;<br/>

<a NAME="E2:21"/><b>then </b><i><font color="Green" title="E10">A2</font></i>: 
(  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c5">g</font> &amp;  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c5">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">f</font> )
 
<b>by </b><i><a class="ref" href="funct_1.html#T55" title="FUNCT_1:th.55">FUNCT_1:55</a></i>;<br/>
<a NAME="E3:21"/><i><font color="Green" title="E11">A3</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_2.html#K1" title="YELLOW_2:func.1">Image</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="waybel10.html#K2" title="WAYBEL10:func.2">|</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span> <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 <font color="Maroon" title="c2">T</font> &amp; the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">R</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 <font color="Maroon" title="c1">S</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="E4:21"/><i><font color="Green" title="E12">A4</font></i>: 
(  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c5">g</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 <font color="Maroon" title="c2">T</font> &amp;  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">f</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 <font color="Maroon" title="c1">S</font> )
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<b>set </b><font color="Maroon" title="c6">h</font> = <font color="Maroon" title="c5">g</font> <a href="waybel10.html#K2" title="WAYBEL10:func.2">|</a> <span class="p1">(<span class="default"><a href="yellow_2.html#K1" title="YELLOW_2:func.1">Image</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="waybel10.html#K2" title="WAYBEL10:func.2">|</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>;<br/>
<a NAME="E5:21"/><i><font color="Green" title="E13">A5</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="waybel10.html#K2" title="WAYBEL10:func.2">|</a> <span class="p2">(<span class="default"><a href="yellow_2.html#K1" title="YELLOW_2:func.1">Image</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="waybel10.html#K2" title="WAYBEL10:func.2">|</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></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_2.html#K1" title="YELLOW_2:func.1">Image</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="waybel10.html#K2" title="WAYBEL10:func.2">|</a> <font color="Maroon" title="c3">R</font></span>)</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="E6:21"/>
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="waybel10.html#K2" title="WAYBEL10:func.2">|</a> <span class="p2">(<span class="default"><a href="yellow_2.html#K1" title="YELLOW_2:func.1">Image</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="waybel10.html#K2" title="WAYBEL10:func.2">|</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <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 <font color="Maroon" title="c3">R</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c7">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="E1:21_1"/>
<font color="Maroon" title="c7">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> <span class="p1">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="waybel10.html#K2" title="WAYBEL10:func.2">|</a> <span class="p2">(<span class="default"><a href="yellow_2.html#K1" title="YELLOW_2:func.1">Image</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="waybel10.html#K2" title="WAYBEL10:func.2">|</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c8">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:21_1"/><i><font color="Green" title="E14">A6</font></i>: 
( <font color="Maroon" title="c8">x</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> <span class="p1">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="waybel10.html#K2" title="WAYBEL10:func.2">|</a> <span class="p2">(<span class="default"><a href="yellow_2.html#K1" title="YELLOW_2:func.1">Image</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="waybel10.html#K2" title="WAYBEL10:func.2">|</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> &amp; <font color="Maroon" title="c7">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="waybel10.html#K2" title="WAYBEL10:func.2">|</a> <span class="p2">(<span class="default"><a href="yellow_2.html#K1" title="YELLOW_2:func.1">Image</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="waybel10.html#K2" title="WAYBEL10:func.2">|</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c9">x</font> = <font color="Maroon" title="c8">x</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_2.html#K1" title="YELLOW_2:func.1">Image</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="waybel10.html#K2" title="WAYBEL10:func.2">|</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span> <b>by </b><i><a class="txt" href="waybel10.html#E3:21_1"><i><font color="Green" title="E14">A6</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon" title="c10">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">R</font><b> such that </b><br/><a NAME="E6:21_1"/><i><font color="Green" title="E15">A7</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="waybel10.html#K2" title="WAYBEL10:func.2">|</a> <font color="Maroon" title="c3">R</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">x</font>
 <b>by </b><i><a class="ref" href="yellow_2.html#T12" title="YELLOW_2:th.12">YELLOW_2:12</a></i>;<br/>
<a NAME="E7:21_1"/>
( <font color="Maroon" title="c7">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">x</font> &amp; <font color="Maroon" title="c9">x</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="c4">f</font> &amp; <font color="Maroon" title="c10">a</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">R</font> )
 
<b>by </b><i><a class="txt" href="waybel10.html#E2:21"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="waybel10.html#E3:21"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="waybel10.html#E4:21"><i><font color="Green" title="E12">A4</font></i></a>, <a class="txt" href="waybel10.html#E5:21"><i><font color="Green" title="E13">A5</font></i></a>, <a class="txt" href="waybel10.html#E3:21_1"><i><font color="Green" title="E14">A6</font></i></a>, <a class="ref" href="waybel10.html#T7" target="_self" title="WAYBEL10:th.7">Th7</a></i>;<br/>
<a NAME="E8:21_1"/><b>then </b>
( <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">x</font> &amp; <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">x</font> &amp; <font color="Maroon" title="c7">y</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="c4">f</font> &amp; <font color="Maroon" title="c10">a</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="c4">f</font> )
 
<b>by </b><i><a class="txt" href="waybel10.html#E1:21"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="waybel10.html#E3:21"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="waybel10.html#E4:21"><i><font color="Green" title="E12">A4</font></i></a>, <a class="txt" href="waybel10.html#E6:21_1"><i><font color="Green" title="E15">A7</font></i></a>, <a class="ref" href="waybel10.html#T7" target="_self" title="WAYBEL10:th.7">Th7</a>, <a class="ref" href="funct_1.html#T54" title="FUNCT_1:th.54">FUNCT_1:54</a></i>;<br/>
<a NAME="E9:21_1"/><b>then </b>
<font color="Maroon" title="c7">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">a</font>
 
<b>by </b><i><a class="txt" href="waybel10.html#E1:21"><i><font color="Green" title="E9">A1</font></i></a>, <a class="ref" href="funct_1.html#D8" title="FUNCT_1:def.8">FUNCT_1:def 8</a></i>;<br/>
<b>hence </b><a NAME="E10:21_1"/>
<font color="Maroon" title="c7">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">R</font>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E7:21"/>
<font color="Maroon" title="c5">g</font> <a href="waybel10.html#K2" title="WAYBEL10:func.2">|</a> <span class="p1">(<span class="default"><a href="yellow_2.html#K1" title="YELLOW_2:func.1">Image</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="waybel10.html#K2" title="WAYBEL10:func.2">|</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span> is   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><a href="yellow_2.html#K1" title="YELLOW_2:func.1">Image</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="waybel10.html#K2" title="WAYBEL10:func.2">|</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">R</font>
 <b>by </b><i><a class="txt" href="waybel10.html#E5:21"><i><font color="Green" title="E13">A5</font></i></a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a>, <a class="ref" href="relset_1.html#T11" title="RELSET_1:th.11">RELSET_1:11</a></i>;<br/>

<a NAME="E8:21"/><i><font color="Green" title="E14">A8</font></i>: 
<font color="Maroon" title="c4">f</font> <a href="waybel10.html#K2" title="WAYBEL10:func.2">|</a> <font color="Maroon" title="c3">R</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>
 
<b>by </b><i><a class="txt" href="waybel10.html#E1:21"><i><font color="Green" title="E9">A1</font></i></a>, <a class="ref" href="waybel10.html#T8" target="_self" title="WAYBEL10:th.8">Th8</a></i>;<br/>
<a NAME="E9:21"/><b>then </b><i><font color="Green" title="E15">A9</font></i>: 
(  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="waybel10.html#K2" title="WAYBEL10:func.2">|</a> <font color="Maroon" title="c3">R</font></span>)</span> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="waybel10.html#K2" title="WAYBEL10:func.2">|</a> <font color="Maroon" title="c3">R</font></span>)</span> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="waybel10.html#K2" title="WAYBEL10:func.2">|</a> <font color="Maroon" title="c3">R</font></span>)</span> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="waybel10.html#K2" title="WAYBEL10:func.2">|</a> <font color="Maroon" title="c3">R</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="funct_1.html#T55" title="FUNCT_1:th.55">FUNCT_1:55</a></i>;<br/>
<a NAME="E10:21"/><i><font color="Green" title="E16">A10</font></i>: 
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="waybel10.html#K2" title="WAYBEL10:func.2">|</a> <font color="Maroon" title="c3">R</font></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_2.html#K1" title="YELLOW_2:func.1">Image</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="waybel10.html#K2" title="WAYBEL10:func.2">|</a> <font color="Maroon" title="c3">R</font></span>)</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/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c7">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:21_2"/><i><font color="Green" title="E17">A11</font></i>: 
<font color="Maroon" title="c7">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_2.html#K1" title="YELLOW_2:func.1">Image</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="waybel10.html#K2" title="WAYBEL10:func.2">|</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon" title="c8">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:21_2"/><i><font color="Green" title="E18">A12</font></i>: 
( <font color="Maroon" title="c8">y</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> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="waybel10.html#K2" title="WAYBEL10:func.2">|</a> <font color="Maroon" title="c3">R</font></span>)</span> &amp; <font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="waybel10.html#K2" title="WAYBEL10:func.2">|</a> <font color="Maroon" title="c3">R</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">y</font> )
 <b>by </b><i><a class="txt" href="waybel10.html#E10:21"><i><font color="Green" title="E16">A10</font></i></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/><a NAME="E4:21_2"/>
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="waybel10.html#K2" title="WAYBEL10:func.2">|</a> <font color="Maroon" title="c3">R</font></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 <font color="Maroon" title="c3">R</font>
 <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="E5:21_2"/><b>then </b>
( <font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">y</font> &amp; <font color="Maroon" title="c8">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="c1">S</font> )
 <b>by </b><i><a class="txt" href="waybel10.html#E3:21"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="waybel10.html#E3:21_2"><i><font color="Green" title="E18">A12</font></i></a>, <a class="ref" href="waybel10.html#T7" target="_self" title="WAYBEL10:th.7">Th7</a></i>;<br/><a NAME="E6:21_2"/><b>then </b>
( <font color="Maroon" title="c8">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font> &amp; <font color="Maroon" title="c8">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="waybel10.html#K2" title="WAYBEL10:func.2">|</a> <font color="Maroon" title="c3">R</font></span>)</span> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font> )
 <b>by </b><i><a class="txt" href="waybel10.html#E1:21"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="waybel10.html#E4:21"><i><font color="Green" title="E12">A4</font></i></a>, <a class="txt" href="waybel10.html#E8:21"><i><font color="Green" title="E14">A8</font></i></a>, <a class="txt" href="waybel10.html#E3:21_2"><i><font color="Green" title="E18">A12</font></i></a>, <a class="ref" href="funct_1.html#T54" title="FUNCT_1:th.54">FUNCT_1:54</a></i>;<br/><b>hence </b><a NAME="E7:21_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="waybel10.html#K2" title="WAYBEL10:func.2">|</a> <span class="p2">(<span class="default"><a href="yellow_2.html#K1" title="YELLOW_2:func.1">Image</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="waybel10.html#K2" title="WAYBEL10:func.2">|</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="waybel10.html#K2" title="WAYBEL10:func.2">|</a> <font color="Maroon" title="c3">R</font></span>)</span> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font>
 <b>by </b><i><a class="txt" href="waybel10.html#E1:21_2"><i><font color="Green" title="E17">A11</font></i></a>, <a class="ref" href="waybel10.html#T7" target="_self" title="WAYBEL10:th.7">Th7</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E12:21"/>
<font color="Maroon" title="c5">g</font> <a href="waybel10.html#K2" title="WAYBEL10:func.2">|</a> <span class="p1">(<span class="default"><a href="yellow_2.html#K1" title="YELLOW_2:func.1">Image</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="waybel10.html#K2" title="WAYBEL10:func.2">|</a> <font color="Maroon" title="c3">R</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="waybel10.html#K2" title="WAYBEL10:func.2">|</a> <font color="Maroon" title="c3">R</font></span>)</span> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a> 
 <b>by </b><i><a class="txt" href="waybel10.html#E5:21"><i><font color="Green" title="E13">A5</font></i></a>, <a class="txt" href="waybel10.html#E9:21"><i><font color="Green" title="E15">A9</font></i></a>, <a class="txt" href="waybel10.html#E10:21"><i><font color="Green" title="E16">A10</font></i></a>, <a class="ref" href="funct_1.html#T9" title="FUNCT_1:th.9">FUNCT_1:9</a></i>;<br/>


</div>
