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<span class="kw">let </span><font color="Maroon" title="c1">i</font> be   non  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</a>  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</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">  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> , <a href="number14.html#K7" title="NUMBER14:func.7">multiples</a> <font color="Maroon" title="c1">i</font> <a href="tarski.html#R3" title="TARSKI:pred.3">are_equipotent</a> </span><br/>

<span class="kw">set </span><font color="Maroon" title="c2">M</font> =  <a href="number14.html#K7" title="NUMBER14:func.7">multiples</a> <font color="Maroon" title="c1">i</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c3">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="c4">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">take </span>
<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>
; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="wellord2.html#D4" onmouseover="rs('wellord2/D4')" onmouseout="rh()">WELLORD2: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"> ( <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> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  &amp;  <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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  &amp;  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">proj2</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="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="number14.html#K7" title="NUMBER14:func.7">multiples</a> <font color="Maroon" title="c1">i</font> )</span><br/>

<span class="kw">thus </span><a NAME="E1:95"/>
<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> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</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"> (  <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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  &amp;  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">proj2</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="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="number14.html#K7" title="NUMBER14:func.7">multiples</a> <font color="Maroon" title="c1">i</font> )</span><br/>

<span class="kw">thus </span><a NAME="E2:95"/>
 <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 href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="valued_1.html#D5" onmouseover="rs('valued_1/D5')" onmouseout="rh()">VALUED_1:def 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">  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">proj2</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="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="number14.html#K7" title="NUMBER14:func.7">multiples</a> <font color="Maroon" title="c1">i</font></span><br/>

<span class="kw">thus </span><a NAME="E3:95"/>
 <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</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="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="number14.html#K7" title="NUMBER14:func.7">multiples</a> <font color="Maroon" title="c1">i</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"> verum</span><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="95_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">thus </span><a NAME="E1:95_1"/>
 <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</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="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="number14.html#K7" title="NUMBER14:func.7">multiples</a> <font color="Maroon" title="c1">i</font>
  <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="xboole_0.html#D10" onmouseover="rs('xboole_0/D10')" onmouseout="rh()">XBOOLE_0:def 10</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">  <a href="number14.html#K7" title="NUMBER14:func.7">multiples</a> <font color="Maroon" title="c1">i</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</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></span><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="95_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c5">y</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="tarski.html#D3" onmouseover="rs('tarski/D3')" onmouseout="rh()">TARSKI:def 3</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="c5">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</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 <font color="Maroon" title="c5">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="number14.html#K7" title="NUMBER14:func.7">multiples</a> <font color="Maroon" title="c1">i</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:95_1_1"/>
<font color="Maroon" title="c5">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</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"> <font color="Maroon" title="c5">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="number14.html#K7" title="NUMBER14:func.7">multiples</a> <font color="Maroon" title="c1">i</font></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E3:95_1_1"/>
<font color="Maroon" title="c6">x</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>
 <span class="kw">and </span><br/><a NAME="E4:95_1_1"/><span class="lab"><font color="Green" title="E66">A1</font></span>: 
<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">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">y</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c7">y</font> = <font color="Maroon" title="c5">y</font> as   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:95_1_1"><span class="lab"><font color="Green" title="E66">A1</font></span></a></span>;<br/>
<a NAME="E6:95_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">x</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">x</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/>
<a NAME="E7:95_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c1">i</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Maroon" title="c7">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:95_1_1"><span class="lab"><font color="Green" title="E66">A1</font></span></a></span>;<br/>
<a NAME="E8:95_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c7">y</font> is    <a href="number14.html#M3" title="NUMBER14:mode.3">Multiple</a> of <font color="Maroon" title="c1">i</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="number14.html#D15" target="_self" onmouseover="rs('number14/D15')" onmouseout="rh()">Def15</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:95_1_1"/>
<font color="Maroon" title="c5">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="number14.html#K7" title="NUMBER14:func.7">multiples</a> <font color="Maroon" title="c1">i</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"> verum</span><br/>


</div><span class="kw">end;</span></div>

<span class="kw">let </span><font color="Maroon" title="c5">y</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="tarski.html#D3" onmouseover="rs('tarski/D3')" onmouseout="rh()">TARSKI:def 3</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="c5">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="number14.html#K7" title="NUMBER14:func.7">multiples</a> <font color="Maroon" title="c1">i</font> or <font color="Maroon" title="c5">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</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> )</span><br/>

<span class="kw">assume </span><a NAME="E2:95_1"/>
<font color="Maroon" title="c5">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="number14.html#K7" title="NUMBER14:func.7">multiples</a> <font color="Maroon" title="c1">i</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"> <font color="Maroon" title="c5">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</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></span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c6">m</font> = <font color="Maroon" title="c5">y</font> as    <a href="number14.html#M3" title="NUMBER14:mode.3">Multiple</a> of <font color="Maroon" title="c1">i</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="number14.html#T61" target="_self" onmouseover="rs('number14/T61')" onmouseout="rh()">Th61</a></span>;<br/>
<a NAME="E4:95_1"/>
<font color="Maroon" title="c1">i</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Maroon" title="c6">m</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="number14.html#D15" target="_self" onmouseover="rs('number14/D15')" onmouseout="rh()">Def15</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">j</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><span class="kw"> such that </span><br/><a NAME="E6:95_1"/><span class="lab"><font color="Green" title="E66">A2</font></span>: 
<font color="Maroon" title="c6">m</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> <font color="Maroon" title="c7">j</font>
 ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c8">j</font> = <font color="Maroon" title="c7">j</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>  <span class="kw">by</span> <span class="lab"><a class="ref" href="int_1.html#D2" onmouseover="rs('int_1/D2')" onmouseout="rh()">INT_1:def 2</a></span>;<br/>
<a NAME="E8:95_1"/><span class="lab"><font color="Green" title="E67">A3</font></span>: 
 <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 href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="valued_1.html#D5" onmouseover="rs('valued_1/D5')" onmouseout="rh()">VALUED_1:def 5</a></span>;<br/>
<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="c8">j</font> = 
<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="c8">j</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/>.= 
<font color="Maroon" title="c5">y</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:95_1"><span class="lab"><font color="Green" title="E66">A2</font></span></a></span>
;<br/>
<span class="kw">hence </span><a NAME="E10:95_1"/>
<font color="Maroon" title="c5">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:95_1"><span class="lab"><font color="Green" title="E67">A3</font></span></a>, <a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</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>
