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<span class="kw">consider </span><font color="Maroon" title="c4">a1</font>, <font color="Maroon" title="c5">a2</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="E2:63_1_1"/><span class="lab"><font color="Green" title="E29">A1</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a1</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c5">a2</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">take </span>
<font color="Maroon" title="c4">a1</font>
; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="exchsort.html#D1" target="_self" title="EXCHSORT:def.1">EXCHSORT:def 1</a> <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="ordinal1.html#V3" title="ORDINAL1:attr.3">ordinal</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>  st  <a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <span class="p1">(<span class="default"><a href="funct_7.html#K10" title="FUNCT_7:func.10">Swap</a> (<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a1</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Olive" title="b1">b</font></span><br/>

<span class="kw">take </span>
<font color="Maroon" title="c5">a2</font>
; <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#K1" title="RELAT_1:func.1">proj1</a> <span class="p1">(<span class="default"><a href="funct_7.html#K10" title="FUNCT_7:func.10">Swap</a> (<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a1</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c5">a2</font></span><br/>

<span class="kw">thus </span><a NAME="E3:63_1_1"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <span class="p1">(<span class="default"><a href="funct_7.html#K10" title="FUNCT_7:func.10">Swap</a> (<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a1</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c5">a2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:63_1_1"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="ref" href="funct_7.html#T99" title="FUNCT_7:th.99">FUNCT_7:99</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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