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<span class="kw">let </span><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</font>, <font color="Maroon" title="c3">C</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">A</font> is    <a href="exchsort.html#M1" title="EXCHSORT:mode.1">permutation</a> of <font color="Maroon" title="c2">B</font> &amp; <font color="Maroon" title="c2">B</font> is    <a href="exchsort.html#M1" title="EXCHSORT:mode.1">permutation</a> of <font color="Maroon" title="c3">C</font> implies <font color="Maroon" title="c1">A</font> is    <a href="exchsort.html#M1" title="EXCHSORT:mode.1">permutation</a> of <font color="Maroon" title="c3">C</font> )</span><br/>





<span class="kw">assume </span><a NAME="E1:70"/><span class="lab"><font color="Green" title="E34">ZZ</font></span>: 
( <font color="Maroon" title="c1">A</font> is    <a href="exchsort.html#M1" title="EXCHSORT:mode.1">permutation</a> of <font color="Maroon" title="c2">B</font> &amp; <font color="Maroon" title="c2">B</font> is    <a href="exchsort.html#M1" title="EXCHSORT:mode.1">permutation</a> of <font color="Maroon" title="c3">C</font> )
 ; <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">A</font> is    <a href="exchsort.html#M1" title="EXCHSORT:mode.1">permutation</a> of <font color="Maroon" title="c3">C</font></span><br/>

<a NAME="E2:70"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">Z0</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">C</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="c2">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/>
<span class="kw">consider </span><font color="Maroon" title="c4">f</font> being   <a href="funct_2.html#NM2" title="FUNCT_2:NM.2">Permutation</a> of <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c2">B</font></span>)</span><span class="kw"> such that </span><br/><a NAME="E4:70"/><span class="lab"><font color="Green" title="E36">Z1</font></span>: 
<font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">B</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c4">f</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:70"><span class="lab"><font color="Green" title="E34">ZZ</font></span></a>, <a class="ref" href="exchsort.html#D9" target="_self" title="EXCHSORT:def.9">PERM</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c5">g</font> being   <a href="funct_2.html#NM2" title="FUNCT_2:NM.2">Permutation</a> of <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">C</font></span>)</span><span class="kw"> such that </span><br/><a NAME="E6:70"/><span class="lab"><font color="Green" title="E37">Z3</font></span>: 
<font color="Maroon" title="c2">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">C</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c5">g</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:70"><span class="lab"><font color="Green" title="E34">ZZ</font></span></a>, <a class="ref" href="exchsort.html#D9" target="_self" title="EXCHSORT:def.9">PERM</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c6">h</font> = <font color="Maroon" title="c5">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">f</font> as   <a href="funct_2.html#NM2" title="FUNCT_2:NM.2">Permutation</a> of <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">C</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:70"><span class="lab"><font color="Green" title="E35">Z0</font></span></a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c6">h</font>
; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="exchsort.html#D9" target="_self" title="EXCHSORT:def.9">EXCHSORT:def 9</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">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">C</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c6">h</font></span><br/>

<span class="kw">thus </span><a NAME="E8:70"/>
<font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">C</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c6">h</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:70"><span class="lab"><font color="Green" title="E36">Z1</font></span></a>, <a class="txt" href="#E6:70"><span class="lab"><font color="Green" title="E37">Z3</font></span></a>, <a class="ref" href="relat_1.html#T36" title="RELAT_1:th.36">RELAT_1:36</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/>


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