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<span class="kw">let </span><font color="Maroon" title="c1">X</font>, <font color="Maroon" title="c2">Y</font> be    <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"> <span class="p1"><a href="funct_3.html#K15" title="FUNCT_3:func.15">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K4" title="RELAT_1:func.4">id</a> <font color="Maroon" title="c1">X</font></span>)</span>,<span class="p2">(<span class="default"><a href="relat_1.html#K4" title="RELAT_1:func.4">id</a> <font color="Maroon" title="c2">Y</font></span>)</span></span><a href="funct_3.html#K15" title="FUNCT_3:func.15">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K4" title="RELAT_1:func.4">id</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span><br/>



<a NAME="E1:84"/>
 <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><a href="funct_3.html#K9" title="FUNCT_3:func.9">pr1</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font>)</span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_3.html#T43" target="_self" onmouseover="rs('funct_3/T43')" onmouseout="rh()">Th43</a></span>;<br/>
<a NAME="E2:84"/><span class="kw">then </span><span class="lab"><font color="Green" title="E48">A1</font></span>: 
<span class="p1">(<span class="default"><a href="relat_1.html#K4" title="RELAT_1:func.4">id</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="funct_3.html#K9" title="FUNCT_3:func.9">pr1</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_3.html#K9" title="FUNCT_3:func.9">pr1</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T53" onmouseover="rs('relat_1/T53')" onmouseout="rh()">RELAT_1:53</a></span>;<br/>
<a NAME="E3:84"/>
 <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><a href="funct_3.html#K10" title="FUNCT_3:func.10">pr2</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font>)</span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_3.html#T45" target="_self" onmouseover="rs('funct_3/T45')" onmouseout="rh()">Th45</a></span>;<br/>
<a NAME="E4:84"/><span class="kw">then </span><span class="lab"><font color="Green" title="E49">A2</font></span>: 
<span class="p1">(<span class="default"><a href="relat_1.html#K4" title="RELAT_1:func.4">id</a> <font color="Maroon" title="c2">Y</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="funct_3.html#K10" title="FUNCT_3:func.10">pr2</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_3.html#K10" title="FUNCT_3:func.10">pr2</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T53" onmouseover="rs('relat_1/T53')" onmouseout="rh()">RELAT_1:53</a></span>;<br/>
<a NAME="E5:84"/>
(  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="relat_1.html#K4" title="RELAT_1:func.4">id</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">X</font> &amp;  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="relat_1.html#K4" title="RELAT_1:func.4">id</a> <font color="Maroon" title="c2">Y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">Y</font> )
 
;<br/>
<span class="kw">hence </span><span class="p1"><a href="funct_3.html#K15" title="FUNCT_3:func.15">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K4" title="RELAT_1:func.4">id</a> <font color="Maroon" title="c1">X</font></span>)</span>,<span class="p2">(<span class="default"><a href="relat_1.html#K4" title="RELAT_1:func.4">id</a> <font color="Maroon" title="c2">Y</font></span>)</span></span><a href="funct_3.html#K15" title="FUNCT_3:func.15">:]</a></span> = 
<span class="p1"><a href="funct_3.html#K13" title="FUNCT_3:func.13">&lt;:</a><span class="default"><span class="p2">(<span class="default"><a href="funct_3.html#K9" title="FUNCT_3:func.9">pr1</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="funct_3.html#K10" title="FUNCT_3:func.10">pr2</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font>)</span>)</span></span><a href="funct_3.html#K13" title="FUNCT_3:func.13">:&gt;</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:84"><span class="lab"><font color="Green" title="E48">A1</font></span></a>, <a class="txt" href="#E4:84"><span class="lab"><font color="Green" title="E49">A2</font></span></a>, <a class="ref" href="funct_3.html#T66" target="_self" onmouseover="rs('funct_3/T66')" onmouseout="rh()">Th66</a></span>
<br/>.= 
 <a href="relat_1.html#K4" title="RELAT_1:func.4">id</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_3.html#T53" target="_self" onmouseover="rs('funct_3/T53')" onmouseout="rh()">Th53</a></span>
;<br/> <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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