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<span class="kw">let </span><font color="Maroon" title="c1">O</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="waybel_0.html#V16" title="WAYBEL_0:attr.16">connected</a>  <a href="orders_2.html#NM1" title="ORDERS_2:NM.1">Poset</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> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>   <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  <a href="exchsort.html#V2" title="EXCHSORT:attr.2">-based</a>  <a href="exchsort.html#NM3" title="EXCHSORT:NM.3">array</a> of <font color="Maroon" title="c1">O</font>  ex <font color="Olive" title="b2">B</font> being    <a href="exchsort.html#M1" title="EXCHSORT:mode.1">permutation</a> of <font color="Olive" title="b1">A</font> st <font color="Olive" title="b2">B</font> is  <a href="exchsort.html#V5" title="EXCHSORT:attr.5">ascending</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">A</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>   <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  <a href="exchsort.html#V2" title="EXCHSORT:attr.2">-based</a>  <a href="exchsort.html#NM3" title="EXCHSORT:NM.3">array</a> of <font color="Maroon" title="c1">O</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">B</font> being    <a href="exchsort.html#M1" title="EXCHSORT:mode.1">permutation</a> of <font color="Maroon" title="c2">A</font> st <font color="Olive" title="b1">B</font> is  <a href="exchsort.html#V5" title="EXCHSORT:attr.5">ascending</a> </span><br/>



<span class="kw">consider </span><font color="Maroon" title="c3">C</font> being   <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  <a href="exchsort.html#V2" title="EXCHSORT:attr.2">-based</a>   <a href="exchsort.html#M2" title="EXCHSORT:mode.2">arr_computation</a> of <font color="Maroon" title="c2">A</font><span class="kw"> such that </span><br/><a NAME="E2:144"/><span class="lab"><font color="Green" title="E79">A0</font></span>: 
<font color="Maroon" title="c3">C</font> is  <a href="exchsort.html#V6" title="EXCHSORT:attr.6">complete</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="exchsort.html#T85" target="_self" title="EXCHSORT:th.85">ThComp</a></span>;<br/>
<a NAME="E3:144"/>
<font color="Maroon" title="c3">C</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="exchsort.html#T76" target="_self" title="EXCHSORT:th.76">MAIN4</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c4">B</font> =  <a href="exchsort.html#K4" title="EXCHSORT:func.4">last</a> <font color="Maroon" title="c3">C</font> as    <a href="exchsort.html#M1" title="EXCHSORT:mode.1">permutation</a> of <font color="Maroon" title="c2">A</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="exchsort.html#T78" target="_self" title="EXCHSORT:th.78">Th83</a></span>;<br/>
<span class="kw">take </span>
<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"> <font color="Maroon" title="c4">B</font> is  <a href="exchsort.html#V5" title="EXCHSORT:attr.5">ascending</a> </span><br/>

<span class="kw">thus </span><a NAME="E5:144"/>
<font color="Maroon" title="c4">B</font> is  <a href="exchsort.html#V5" title="EXCHSORT:attr.5">ascending</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:144"><span class="lab"><font color="Green" title="E79">A0</font></span></a>, <a class="ref" href="exchsort.html#D15" target="_self" title="EXCHSORT:def.15">COMPL</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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