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

<span class="kw">let </span><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">A</font>, <font color="Olive" title="b2">B</font> being   <a href="exchsort.html#NM1" title="EXCHSORT:NM.1">array</a>  st <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Olive" title="b1">A</font> &amp; <font color="Maroon" title="c2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Olive" title="b1">A</font> &amp; <font color="Olive" title="b1">A</font> is    <a href="exchsort.html#M1" title="EXCHSORT:mode.1">permutation</a> of <font color="Olive" title="b2">B</font> holds <br/>(  <a href="funct_7.html#K10" title="FUNCT_7:func.10">Swap</a> (<font color="Olive" title="b1">A</font>,<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>) is    <a href="exchsort.html#M1" title="EXCHSORT:mode.1">permutation</a> of <font color="Olive" title="b2">B</font> &amp; <font color="Olive" title="b1">A</font> is    <a href="exchsort.html#M1" title="EXCHSORT:mode.1">permutation</a> of  <a href="funct_7.html#K10" title="FUNCT_7:func.10">Swap</a> (<font color="Olive" title="b2">B</font>,<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>) )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">A</font>, <font color="Maroon" title="c4">B</font> be   <a href="exchsort.html#NM1" title="EXCHSORT:NM.1">array</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">A</font> &amp; <font color="Maroon" title="c2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">A</font> &amp; <font color="Maroon" title="c3">A</font> is    <a href="exchsort.html#M1" title="EXCHSORT:mode.1">permutation</a> of <font color="Maroon" title="c4">B</font> implies (  <a href="funct_7.html#K10" title="FUNCT_7:func.10">Swap</a> (<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>) is    <a href="exchsort.html#M1" title="EXCHSORT:mode.1">permutation</a> of <font color="Maroon" title="c4">B</font> &amp; <font color="Maroon" title="c3">A</font> is    <a href="exchsort.html#M1" title="EXCHSORT:mode.1">permutation</a> of  <a href="funct_7.html#K10" title="FUNCT_7:func.10">Swap</a> (<font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>) ) )</span><br/>







<span class="kw">set </span><font color="Maroon" title="c5">X</font> =  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">A</font>;<br/>
<span class="kw">assume </span><a NAME="E1:77"/><span class="lab"><font color="Green" title="E37">Z0</font></span>: 
( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">A</font> &amp; <font color="Maroon" title="c2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">A</font> &amp; <font color="Maroon" title="c3">A</font> is    <a href="exchsort.html#M1" title="EXCHSORT:mode.1">permutation</a> of <font color="Maroon" title="c4">B</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="funct_7.html#K10" title="FUNCT_7:func.10">Swap</a> (<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>) is    <a href="exchsort.html#M1" title="EXCHSORT:mode.1">permutation</a> of <font color="Maroon" title="c4">B</font> &amp; <font color="Maroon" title="c3">A</font> is    <a href="exchsort.html#M1" title="EXCHSORT:mode.1">permutation</a> of  <a href="funct_7.html#K10" title="FUNCT_7:func.10">Swap</a> (<font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>) )</span><br/>

<a NAME="E2:77"/><span class="kw">then </span>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="exchsort.html#T37" target="_self" title="EXCHSORT:th.37">ThDom</a></span>;<br/>
<a NAME="E3:77"/><span class="kw">then </span>
(  <a href="funct_7.html#K10" title="FUNCT_7:func.10">Swap</a> (<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>) is    <a href="exchsort.html#M1" title="EXCHSORT:mode.1">permutation</a> of <font color="Maroon" title="c3">A</font> &amp; <font color="Maroon" title="c4">B</font> is    <a href="exchsort.html#M1" title="EXCHSORT:mode.1">permutation</a> of  <a href="funct_7.html#K10" title="FUNCT_7:func.10">Swap</a> (<font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>) )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:77"><span class="lab"><font color="Green" title="E37">Z0</font></span></a>, <a class="ref" href="exchsort.html#T43" target="_self" title="EXCHSORT:th.43">Th13</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:77"/>
(  <a href="funct_7.html#K10" title="FUNCT_7:func.10">Swap</a> (<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>) is    <a href="exchsort.html#M1" title="EXCHSORT:mode.1">permutation</a> of <font color="Maroon" title="c4">B</font> &amp; <font color="Maroon" title="c3">A</font> is    <a href="exchsort.html#M1" title="EXCHSORT:mode.1">permutation</a> of  <a href="funct_7.html#K10" title="FUNCT_7:func.10">Swap</a> (<font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:77"><span class="lab"><font color="Green" title="E37">Z0</font></span></a>, <a class="ref" href="exchsort.html#T40" target="_self" title="EXCHSORT:th.40">ThTr</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
