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<span class="kw">set </span><font color="Maroon" title="c2">I</font> =  <a href="relat_1.html#K4" title="RELAT_1:func.4">id</a> <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>;<br/>
<span class="kw">set </span><font color="Maroon" title="c3">f</font> = <font color="Maroon" title="c1">i</font> <a href="valued_1.html#K24" title="VALUED_1:func.24">(#)</a> <span class="p1">(<span class="default"><a href="relat_1.html#K4" title="RELAT_1:func.4">id</a> <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a></span>)</span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c4">x1</font>, <font color="Maroon" title="c5">x2</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="funct_1.html#D4" onmouseover="rs('funct_1/D4')" onmouseout="rh()">FUNCT_1:def 4</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"> (  not <font color="Maroon" title="c4">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="xtuple_0.html#K9" title="XTUPLE_0:func.9">proj1</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="valued_1.html#K24" title="VALUED_1:func.24">(#)</a> <span class="p2">(<span class="default"><a href="relat_1.html#K4" title="RELAT_1:func.4">id</a> <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a></span>)</span></span>)</span> or  not <font color="Maroon" title="c5">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="xtuple_0.html#K9" title="XTUPLE_0:func.9">proj1</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="valued_1.html#K24" title="VALUED_1:func.24">(#)</a> <span class="p2">(<span class="default"><a href="relat_1.html#K4" title="RELAT_1:func.4">id</a> <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a></span>)</span></span>)</span> or  not <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="valued_1.html#K24" title="VALUED_1:func.24">(#)</a> <span class="p2">(<span class="default"><a href="relat_1.html#K4" title="RELAT_1:func.4">id</a> <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="valued_1.html#K24" title="VALUED_1:func.24">(#)</a> <span class="p2">(<span class="default"><a href="relat_1.html#K4" title="RELAT_1:func.4">id</a> <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x2</font> or <font color="Maroon" title="c4">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">x2</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:94_1_1"/>
( <font color="Maroon" title="c4">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="valued_1.html#K24" title="VALUED_1:func.24">(#)</a> <span class="p2">(<span class="default"><a href="relat_1.html#K4" title="RELAT_1:func.4">id</a> <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a></span>)</span></span>)</span> &amp; <font color="Maroon" title="c5">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="valued_1.html#K24" title="VALUED_1:func.24">(#)</a> <span class="p2">(<span class="default"><a href="relat_1.html#K4" title="RELAT_1:func.4">id</a> <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a></span>)</span></span>)</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"> (  not <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="valued_1.html#K24" title="VALUED_1:func.24">(#)</a> <span class="p2">(<span class="default"><a href="relat_1.html#K4" title="RELAT_1:func.4">id</a> <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="valued_1.html#K24" title="VALUED_1:func.24">(#)</a> <span class="p2">(<span class="default"><a href="relat_1.html#K4" title="RELAT_1:func.4">id</a> <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x2</font> or <font color="Maroon" title="c4">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">x2</font> )</span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c6">x1</font> = <font color="Maroon" title="c4">x1</font>, <font color="Maroon" title="c7">x2</font> = <font color="Maroon" title="c5">x2</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  ;<br/>
<a NAME="E3:94_1_1"/>
( <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="valued_1.html#K24" title="VALUED_1:func.24">(#)</a> <span class="p2">(<span class="default"><a href="relat_1.html#K4" title="RELAT_1:func.4">id</a> <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">i</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K4" title="RELAT_1:func.4">id</a> <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x1</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="valued_1.html#K24" title="VALUED_1:func.24">(#)</a> <span class="p2">(<span class="default"><a href="relat_1.html#K4" title="RELAT_1:func.4">id</a> <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">i</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K4" title="RELAT_1:func.4">id</a> <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x2</font></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="valued_1.html#T6" onmouseover="rs('valued_1/T6')" onmouseout="rh()">VALUED_1:6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:94_1_1"/>
(  not <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="valued_1.html#K24" title="VALUED_1:func.24">(#)</a> <span class="p2">(<span class="default"><a href="relat_1.html#K4" title="RELAT_1:func.4">id</a> <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="valued_1.html#K24" title="VALUED_1:func.24">(#)</a> <span class="p2">(<span class="default"><a href="relat_1.html#K4" title="RELAT_1:func.4">id</a> <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x2</font> or <font color="Maroon" title="c4">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">x2</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xcmplx_1.html#T5" onmouseover="rs('xcmplx_1/T5')" onmouseout="rh()">XCMPLX_1:5</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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