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<span class="kw">let </span><font color="Maroon" title="c1">i</font>, <font color="Maroon" title="c2">j</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">D</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">f</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Olive" title="b1">D</font>  st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">i</font> &amp; <font color="Maroon" title="c1">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b2">f</font> &amp; 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">j</font> &amp; <font color="Maroon" title="c2">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b2">f</font> holds <br/>( <span class="p1">(<span class="default"><a href="finseq_7.html#K2" title="FINSEQ_7:func.2">Swap</a> (<font color="Olive" title="b2">f</font>,<font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">j</font> &amp; <span class="p1">(<span class="default"><a href="finseq_7.html#K2" title="FINSEQ_7:func.2">Swap</a> (<font color="Olive" title="b2">f</font>,<font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">D</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">f</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c3">D</font>  st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">i</font> &amp; <font color="Maroon" title="c1">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">f</font> &amp; 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">j</font> &amp; <font color="Maroon" title="c2">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">f</font> holds <br/>( <span class="p1">(<span class="default"><a href="finseq_7.html#K2" title="FINSEQ_7:func.2">Swap</a> (<font color="Olive" title="b1">f</font>,<font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">j</font> &amp; <span class="p1">(<span class="default"><a href="finseq_7.html#K2" title="FINSEQ_7:func.2">Swap</a> (<font color="Olive" title="b1">f</font>,<font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">f</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c3">D</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">i</font> &amp; <font color="Maroon" title="c1">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">f</font> &amp; 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">j</font> &amp; <font color="Maroon" title="c2">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">f</font> implies ( <span class="p1">(<span class="default"><a href="finseq_7.html#K2" title="FINSEQ_7:func.2">Swap</a> (<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">j</font> &amp; <span class="p1">(<span class="default"><a href="finseq_7.html#K2" title="FINSEQ_7:func.2">Swap</a> (<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font> ) )</span><br/>







<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:14"/><span class="lab"><font color="Green" title="E10">A1</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">i</font>
 <span class="kw">and </span><br/><a NAME="E2:14"/><span class="lab"><font color="Green" title="E11">A2</font></span>: 
<font color="Maroon" title="c1">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">f</font>
 <span class="kw">and </span><br/><a NAME="E3:14"/><span class="lab"><font color="Green" title="E12">A3</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">j</font>
 <span class="kw">and </span><br/><a NAME="E4:14"/><span class="lab"><font color="Green" title="E13">A4</font></span>: 
<font color="Maroon" title="c2">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">f</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="finseq_7.html#K2" title="FINSEQ_7:func.2">Swap</a> (<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">j</font> &amp; <span class="p1">(<span class="default"><a href="finseq_7.html#K2" title="FINSEQ_7:func.2">Swap</a> (<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font> )</span><br/>

<a NAME="E5:14"/><span class="lab"><font color="Green" title="E14">A5</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="finseq_7.html#K1" title="FINSEQ_7:func.1">Replace</a> (<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c1">i</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c2">j</font></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">f</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_7.html#T5" onmouseover="rs('finseq_7/T5')" onmouseout="rh()">FINSEQ_7:5</a></span>;<br/>
<a NAME="E6:14"/><span class="lab"><font color="Green" title="E15">A6</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="finseq_7.html#K2" title="FINSEQ_7:func.2">Swap</a> (<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">f</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_7.html#T18" onmouseover="rs('finseq_7/T18')" onmouseout="rh()">FINSEQ_7:18</a></span>;<br/>
<a NAME="E7:14"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="finseq_7.html#K2" title="FINSEQ_7:func.2">Swap</a> (<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c2">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_7.html#K2" title="FINSEQ_7:func.2">Swap</a> (<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">j</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14"><span class="lab"><font color="Green" title="E12">A3</font></span></a>, <a class="txt" href="#E4:14"><span class="lab"><font color="Green" title="E13">A4</font></span></a>, <a class="ref" href="finseq_4.html#T15" onmouseover="rs('finseq_4/T15')" onmouseout="rh()">FINSEQ_4:15</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E16">A7</font></span>: <span class="p1">(<span class="default"><a href="finseq_7.html#K2" title="FINSEQ_7:func.2">Swap</a> (<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">j</font> = 
<span class="p1">(<span class="default"><a href="finseq_7.html#K1" title="FINSEQ_7:func.1">Replace</a> (<span class="p2">(<span class="default"><a href="finseq_7.html#K1" title="FINSEQ_7:func.1">Replace</a> (<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c1">i</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c2">j</font></span>)</span>)</span>)</span>,<font color="Maroon" title="c2">j</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c1">i</font></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c2">j</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="txt" href="#E2:14"><span class="lab"><font color="Green" title="E11">A2</font></span></a>, <a class="txt" href="#E3:14"><span class="lab"><font color="Green" title="E12">A3</font></span></a>, <a class="txt" href="#E4:14"><span class="lab"><font color="Green" title="E13">A4</font></span></a>, <a class="ref" href="finseq_7.html#D2" onmouseover="rs('finseq_7/D2')" onmouseout="rh()">FINSEQ_7:def 2</a></span>
<br/>.= 
<font color="Maroon" title="c4">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c1">i</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14"><span class="lab"><font color="Green" title="E12">A3</font></span></a>, <a class="txt" href="#E4:14"><span class="lab"><font color="Green" title="E13">A4</font></span></a>, <a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E14">A5</font></span></a>, <a class="ref" href="finseq_7.html#T8" onmouseover="rs('finseq_7/T8')" onmouseout="rh()">FINSEQ_7:8</a></span>
<br/>.= 
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="txt" href="#E2:14"><span class="lab"><font color="Green" title="E11">A2</font></span></a>, <a class="ref" href="finseq_4.html#T15" onmouseover="rs('finseq_4/T15')" onmouseout="rh()">FINSEQ_4:15</a></span>
;<br/>
<a NAME="E9:14"/><span class="lab"><font color="Green" title="E17">A8</font></span>: 
 <a href="finseq_7.html#K2" title="FINSEQ_7:func.2">Swap</a> (<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_7.html#K2" title="FINSEQ_7:func.2">Swap</a> (<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c2">j</font>,<font color="Maroon" title="c1">i</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_7.html#T21" onmouseover="rs('finseq_7/T21')" onmouseout="rh()">FINSEQ_7:21</a></span>;<br/>
<a NAME="E10:14"/><span class="lab"><font color="Green" title="E18">A9</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="finseq_7.html#K1" title="FINSEQ_7:func.1">Replace</a> (<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c2">j</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c1">i</font></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">f</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_7.html#T5" onmouseover="rs('finseq_7/T5')" onmouseout="rh()">FINSEQ_7:5</a></span>;<br/>
<a NAME="E11:14"/>
<span class="p1">(<span class="default"><a href="finseq_7.html#K2" title="FINSEQ_7:func.2">Swap</a> (<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_7.html#K2" title="FINSEQ_7:func.2">Swap</a> (<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="txt" href="#E2:14"><span class="lab"><font color="Green" title="E11">A2</font></span></a>, <a class="txt" href="#E6:14"><span class="lab"><font color="Green" title="E15">A6</font></span></a>, <a class="ref" href="finseq_4.html#T15" onmouseover="rs('finseq_4/T15')" onmouseout="rh()">FINSEQ_4:15</a></span>;<br/>
<span class="kw">then </span><span class="p1">(<span class="default"><a href="finseq_7.html#K2" title="FINSEQ_7:func.2">Swap</a> (<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font> = 
<span class="p1">(<span class="default"><a href="finseq_7.html#K1" title="FINSEQ_7:func.1">Replace</a> (<span class="p2">(<span class="default"><a href="finseq_7.html#K1" title="FINSEQ_7:func.1">Replace</a> (<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c2">j</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c1">i</font></span>)</span>)</span>)</span>,<font color="Maroon" title="c1">i</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c2">j</font></span>)</span>)</span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c1">i</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="txt" href="#E2:14"><span class="lab"><font color="Green" title="E11">A2</font></span></a>, <a class="txt" href="#E3:14"><span class="lab"><font color="Green" title="E12">A3</font></span></a>, <a class="txt" href="#E4:14"><span class="lab"><font color="Green" title="E13">A4</font></span></a>, <a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E17">A8</font></span></a>, <a class="ref" href="finseq_7.html#D2" onmouseover="rs('finseq_7/D2')" onmouseout="rh()">FINSEQ_7:def 2</a></span>
<br/>.= 
<font color="Maroon" title="c4">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c2">j</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="txt" href="#E2:14"><span class="lab"><font color="Green" title="E11">A2</font></span></a>, <a class="txt" href="#E10:14"><span class="lab"><font color="Green" title="E18">A9</font></span></a>, <a class="ref" href="finseq_7.html#T8" onmouseover="rs('finseq_7/T8')" onmouseout="rh()">FINSEQ_7:8</a></span>
<br/>.= 
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">j</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14"><span class="lab"><font color="Green" title="E12">A3</font></span></a>, <a class="txt" href="#E4:14"><span class="lab"><font color="Green" title="E13">A4</font></span></a>, <a class="ref" href="finseq_4.html#T15" onmouseover="rs('finseq_4/T15')" onmouseout="rh()">FINSEQ_4:15</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E13:14"/>
( <span class="p1">(<span class="default"><a href="finseq_7.html#K2" title="FINSEQ_7:func.2">Swap</a> (<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">j</font> &amp; <span class="p1">(<span class="default"><a href="finseq_7.html#K2" title="FINSEQ_7:func.2">Swap</a> (<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">i</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:14"><span class="lab"><font color="Green" title="E16">A7</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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