<?xml version="1.0"?>
<div class="add">

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="133_1_1_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:133_1_1_1"/>
( ( <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c1">F</font> &amp; <font color="Maroon" title="c3">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c1">F</font> ) or  not <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c1">F</font> or  not <font color="Maroon" title="c3">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c1">F</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="133_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:133_1_1_1_1"/>
( <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c1">F</font> &amp; <font color="Maroon" title="c3">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c1">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"> (  <a href="funct_7.html#K9" title="FUNCT_7:func.9">Swap</a> (<font color="Maroon" title="c1">F</font>,<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>) is  <a href="relat_1.html#V1" title="RELAT_1:attr.1">Relation-like</a>  &amp;  <a href="funct_7.html#K9" title="FUNCT_7:func.9">Swap</a> (<font color="Maroon" title="c1">F</font>,<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>) is  <a href="funct_1.html#V1" title="FUNCT_1:attr.1">Function-like</a>  )</span><br/><div class="add"><a NAME="E2:133_1_1_1_1"/><span class="kw">then </span>
 <a href="funct_7.html#K9" title="FUNCT_7:func.9">Swap</a> (<font color="Maroon" title="c1">F</font>,<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="funct_7.html#K1" title="FUNCT_7:func.1">+*</a> (<font color="Maroon" title="c2">x</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">y</font></span>)</span>)</span>)</span> <a href="funct_7.html#K1" title="FUNCT_7:func.1">+*</a> (<font color="Maroon" title="c3">y</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">x</font></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_7.html#D12" target="_self" onmouseover="rs('funct_7/D12')" onmouseout="rh()">Def11</a></span>;<br/><span class="kw">hence </span><a NAME="E3:133_1_1_1_1"/>
(  <a href="funct_7.html#K9" title="FUNCT_7:func.9">Swap</a> (<font color="Maroon" title="c1">F</font>,<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>) is  <a href="relat_1.html#V1" title="RELAT_1:attr.1">Relation-like</a>  &amp;  <a href="funct_7.html#K9" title="FUNCT_7:func.9">Swap</a> (<font color="Maroon" title="c1">F</font>,<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>) is  <a href="funct_1.html#V1" title="FUNCT_1:attr.1">Function-like</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"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="133_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:133_1_1_1_2"/>
(  not <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c1">F</font> or  not <font color="Maroon" title="c3">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c1">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"> (  <a href="funct_7.html#K9" title="FUNCT_7:func.9">Swap</a> (<font color="Maroon" title="c1">F</font>,<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>) is  <a href="relat_1.html#V1" title="RELAT_1:attr.1">Relation-like</a>  &amp;  <a href="funct_7.html#K9" title="FUNCT_7:func.9">Swap</a> (<font color="Maroon" title="c1">F</font>,<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>) is  <a href="funct_1.html#V1" title="FUNCT_1:attr.1">Function-like</a>  )</span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:133_1_1_1_2"/>
(  <a href="funct_7.html#K9" title="FUNCT_7:func.9">Swap</a> (<font color="Maroon" title="c1">F</font>,<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>) is  <a href="relat_1.html#V1" title="RELAT_1:attr.1">Relation-like</a>  &amp;  <a href="funct_7.html#K9" title="FUNCT_7:func.9">Swap</a> (<font color="Maroon" title="c1">F</font>,<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>) is  <a href="funct_1.html#V1" title="FUNCT_1:attr.1">Function-like</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_7.html#D12" target="_self" onmouseover="rs('funct_7/D12')" onmouseout="rh()">Def11</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/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div>
