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<span class="kw">let </span><font color="Maroon" title="c1">s</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">s</font> is  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  <a href="exchsort.html#V2" title="EXCHSORT:attr.2">-based</a>  implies <font color="Maroon" title="c1">s</font> is  <a href="ordinal1.html#V5" title="ORDINAL1:attr.5">T-Sequence-like</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:27_1_1"/><span class="lab"><font color="Green" title="E17">Z0</font></span>: 
 for <font color="Olive" title="b1">b</font> being   <a href="ordinal1.html#V3" title="ORDINAL1:attr.3">ordinal</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>   st <font color="Olive" title="b1">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <font color="Maroon" title="c1">s</font> holds <br/>(  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <font color="Maroon" title="c1">s</font> &amp;  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Olive" title="b1">b</font> )
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="exchsort.html#D2" target="_self" title="EXCHSORT:def.2">EXCHSORT:def 2</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">s</font> is  <a href="ordinal1.html#V5" title="ORDINAL1:attr.5">T-Sequence-like</a> </span><br/>

<span class="kw">consider </span><font color="Maroon" title="c2">c</font>, <font color="Maroon" title="c3">a</font> being   <a href="ordinal1.html#V3" title="ORDINAL1:attr.3">ordinal</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> <span class="kw"> such that </span><br/><a NAME="E3:27_1_1"/><span class="lab"><font color="Green" title="E18">A1</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">c</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c3">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="exchsort.html#D1" target="_self" title="EXCHSORT:def.1">SEG</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">x</font> =  the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">c</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c3">a</font>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:27_1_1_1"/><span class="lab"><font color="Green" title="E19">A2</font></span>: 
<font color="Maroon" title="c2">c</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c3">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">c</font></span><br/><a NAME="E2:27_1_1_1"/><span class="kw">then </span>
 the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">c</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>;<br/><a NAME="E3:27_1_1_1"/><span class="kw">then </span>
 <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  <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="c1">s</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:27_1_1"><span class="lab"><font color="Green" title="E17">Z0</font></span></a>, <a class="txt" href="#E3:27_1_1"><span class="lab"><font color="Green" title="E18">A1</font></span></a>, <a class="txt" href="#E1:27_1_1_1"><span class="lab"><font color="Green" title="E19">A2</font></span></a></span>;<br/><a NAME="E4:27_1_1_1"/><span class="kw">then </span>
 <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  <a href="aofa_000.html#NR1" title="AOFA_000:NR.1">nin</a> <font color="Maroon" title="c3">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:27_1_1"><span class="lab"><font color="Green" title="E18">A1</font></span></a>, <a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>;<br/><a NAME="E5:27_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">a</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal6.html#T4" title="ORDINAL6:th.4">ORDINAL6:4</a></span>;<br/><a NAME="E6:27_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> 
 ;<br/><span class="kw">hence </span><a NAME="E7:27_1_1_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:27_1_1"><span class="lab"><font color="Green" title="E18">A1</font></span></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><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E5:27_1_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">s</font> is  <a href="ordinal1.html#V3" title="ORDINAL1:attr.3">ordinal</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:27_1_1"><span class="lab"><font color="Green" title="E18">A1</font></span></a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="ordinal1.html#D7" title="ORDINAL1:def.7">ORDINAL1:def 7</a> <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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