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<span class="kw">let </span><font color="Maroon" title="c1">m</font>, <font color="Maroon" title="c2">n</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"> <font color="Maroon" title="c1">m</font> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <font color="Maroon" title="c2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">m</font> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <span class="p1"><a href="int_2.html#K1" title="INT_2:func.1">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">m</font></span>)</span></span><a href="int_2.html#K1" title="INT_2:func.1">.|</a></span></span><br/>



<span class="kw">set </span><font color="Maroon" title="c3">x</font> = <font color="Maroon" title="c1">m</font> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <font color="Maroon" title="c2">n</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">y</font> = <font color="Maroon" title="c1">m</font> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <span class="p1"><a href="int_2.html#K1" title="INT_2:func.1">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">m</font></span>)</span></span><a href="int_2.html#K1" title="INT_2:func.1">.|</a></span>;<br/>
<a NAME="E1:119"/><span class="lab"><font color="Green" title="E98">A1</font></span>: 
<font color="Maroon" title="c1">m</font> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <font color="Maroon" title="c2">n</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c1">m</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_d.html#D5" onmouseover="rs('nat_d/D5')" onmouseout="rh()">NAT_D:def 5</a></span>;<br/>
<a NAME="E2:119"/><span class="lab"><font color="Green" title="E99">A2</font></span>: 
<font color="Maroon" title="c1">m</font> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <font color="Maroon" title="c2">n</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c2">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_d.html#D5" onmouseover="rs('nat_d/D5')" onmouseout="rh()">NAT_D:def 5</a></span>;<br/>
<a NAME="E3:119"/><span class="lab"><font color="Green" title="E100">A3</font></span>: 
<font color="Maroon" title="c1">m</font> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <span class="p1"><a href="int_2.html#K1" title="INT_2:func.1">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">m</font></span>)</span></span><a href="int_2.html#K1" title="INT_2:func.1">.|</a></span> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c1">m</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_d.html#D5" onmouseover="rs('nat_d/D5')" onmouseout="rh()">NAT_D:def 5</a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="119_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="E1:119_1"/>
( <font color="Maroon" title="c2">n</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">m</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  or <font color="Maroon" title="c2">n</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="119_1_1"><span class="kw">suppose </span></a><a NAME="E1:119_1_1"/>
<font color="Maroon" title="c2">n</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">m</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</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">m</font> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <font color="Maroon" title="c2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">m</font> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <span class="p1"><a href="int_2.html#K1" title="INT_2:func.1">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">m</font></span>)</span></span><a href="int_2.html#K1" title="INT_2:func.1">.|</a></span></span><br/><div class="add"><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c5">nm</font> = <font color="Maroon" title="c2">n</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">m</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="int_1.html#T3" onmouseover="rs('int_1/T3')" onmouseout="rh()">INT_1:3</a></span>;<br/><a NAME="E3:119_1_1"/><span class="lab"><font color="Green" title="E101">A4</font></span>: 
<span class="p1"><a href="int_2.html#K1" title="INT_2:func.1">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">m</font></span>)</span></span><a href="int_2.html#K1" title="INT_2:func.1">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">nm</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="absvalue.html#D1" onmouseover="rs('absvalue/D1')" onmouseout="rh()">ABSVALUE:def 1</a></span>;<br/><a NAME="E4:119_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c1">m</font> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <span class="p1"><a href="int_2.html#K1" title="INT_2:func.1">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">m</font></span>)</span></span><a href="int_2.html#K1" title="INT_2:func.1">.|</a></span> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c5">nm</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_d.html#D5" onmouseover="rs('nat_d/D5')" onmouseout="rh()">NAT_D:def 5</a></span>;<br/><a NAME="E5:119_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c1">m</font> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <span class="p1"><a href="int_2.html#K1" title="INT_2:func.1">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">m</font></span>)</span></span><a href="int_2.html#K1" title="INT_2:func.1">.|</a></span> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c5">nm</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c1">m</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:119"><span class="lab"><font color="Green" title="E100">A3</font></span></a>, <a class="ref" href="nat_d.html#T8" onmouseover="rs('nat_d/T8')" onmouseout="rh()">NAT_D:8</a></span>;<br/><a NAME="E6:119_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E102">A5</font></span>: 
<font color="Maroon" title="c1">m</font> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <span class="p1"><a href="int_2.html#K1" title="INT_2:func.1">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">m</font></span>)</span></span><a href="int_2.html#K1" title="INT_2:func.1">.|</a></span> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c1">m</font> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <font color="Maroon" title="c2">n</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:119"><span class="lab"><font color="Green" title="E100">A3</font></span></a>, <a class="ref" href="nat_d.html#D5" onmouseover="rs('nat_d/D5')" onmouseout="rh()">NAT_D:def 5</a></span>;<br/><a NAME="E7:119_1_1"/>
<font color="Maroon" title="c1">m</font> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <font color="Maroon" title="c2">n</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Maroon" title="c2">n</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">m</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:119"><span class="lab"><font color="Green" title="E98">A1</font></span></a>, <a class="txt" href="#E2:119"><span class="lab"><font color="Green" title="E99">A2</font></span></a>, <a class="ref" href="prepower.html#T94" target="_self" onmouseover="rs('prepower/T94')" onmouseout="rh()">Th94</a></span>;<br/><a NAME="E8:119_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c1">m</font> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <font color="Maroon" title="c2">n</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c1">m</font> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <span class="p1"><a href="int_2.html#K1" title="INT_2:func.1">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">m</font></span>)</span></span><a href="int_2.html#K1" title="INT_2:func.1">.|</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:119"><span class="lab"><font color="Green" title="E98">A1</font></span></a>, <a class="txt" href="#E3:119_1_1"><span class="lab"><font color="Green" title="E101">A4</font></span></a>, <a class="ref" href="nat_d.html#D5" onmouseover="rs('nat_d/D5')" onmouseout="rh()">NAT_D:def 5</a></span>;<br/><span class="kw">hence </span><a NAME="E9:119_1_1"/>
<font color="Maroon" title="c1">m</font> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <font color="Maroon" title="c2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">m</font> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <span class="p1"><a href="int_2.html#K1" title="INT_2:func.1">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">m</font></span>)</span></span><a href="int_2.html#K1" title="INT_2:func.1">.|</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:119_1_1"><span class="lab"><font color="Green" title="E102">A5</font></span></a>, <a class="ref" href="nat_d.html#T5" onmouseover="rs('nat_d/T5')" onmouseout="rh()">NAT_D: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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="119_1_2"><span class="kw">suppose </span></a><a NAME="E1:119_1_2"/><span class="lab"><font color="Green" title="E101">A6</font></span>: 
<font color="Maroon" title="c2">n</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</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">m</font> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <font color="Maroon" title="c2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">m</font> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <span class="p1"><a href="int_2.html#K1" title="INT_2:func.1">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">m</font></span>)</span></span><a href="int_2.html#K1" title="INT_2:func.1">.|</a></span></span><br/><div class="add"><span class="kw">reconsider </span><font color="Maroon" title="c5">nn</font> = <font color="Maroon" title="c2">n</font> as   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> ;<br/><span class="lab"><font color="Green" title="E102">A7</font></span>: <span class="p1"><a href="int_2.html#K1" title="INT_2:func.1">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">m</font></span>)</span></span><a href="int_2.html#K1" title="INT_2:func.1">.|</a></span> = 
 <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">m</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:119_1_2"><span class="lab"><font color="Green" title="E101">A6</font></span></a>, <a class="ref" href="absvalue.html#D1" onmouseover="rs('absvalue/D1')" onmouseout="rh()">ABSVALUE:def 1</a></span>
<br/>.= 
<font color="Maroon" title="c1">m</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c2">n</font>

;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c6">mn</font> = <font color="Maroon" title="c1">m</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c2">n</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  ;<br/><a NAME="E5:119_1_2"/>
<font color="Maroon" title="c1">m</font> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <span class="p1"><a href="int_2.html#K1" title="INT_2:func.1">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">m</font></span>)</span></span><a href="int_2.html#K1" title="INT_2:func.1">.|</a></span> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c6">mn</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:119_1_2"><span class="lab"><font color="Green" title="E102">A7</font></span></a>, <a class="ref" href="nat_d.html#D5" onmouseover="rs('nat_d/D5')" onmouseout="rh()">NAT_D:def 5</a></span>;<br/><a NAME="E6:119_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c1">m</font> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <span class="p1"><a href="int_2.html#K1" title="INT_2:func.1">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">m</font></span>)</span></span><a href="int_2.html#K1" title="INT_2:func.1">.|</a></span> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Maroon" title="c6">mn</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">m</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:119"><span class="lab"><font color="Green" title="E100">A3</font></span></a>, <a class="ref" href="prepower.html#T94" target="_self" onmouseover="rs('prepower/T94')" onmouseout="rh()">Th94</a></span>;<br/><a NAME="E7:119_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c1">m</font> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <span class="p1"><a href="int_2.html#K1" title="INT_2:func.1">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">m</font></span>)</span></span><a href="int_2.html#K1" title="INT_2:func.1">.|</a></span> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Maroon" title="c5">nn</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="int_2.html#T10" onmouseover="rs('int_2/T10')" onmouseout="rh()">INT_2:10</a></span>;<br/><a NAME="E8:119_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E103">A8</font></span>: 
<font color="Maroon" title="c1">m</font> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <span class="p1"><a href="int_2.html#K1" title="INT_2:func.1">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">m</font></span>)</span></span><a href="int_2.html#K1" title="INT_2:func.1">.|</a></span> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c1">m</font> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <font color="Maroon" title="c2">n</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:119"><span class="lab"><font color="Green" title="E100">A3</font></span></a>, <a class="ref" href="nat_d.html#D5" onmouseover="rs('nat_d/D5')" onmouseout="rh()">NAT_D:def 5</a></span>;<br/><a NAME="E9:119_1_2"/>
<font color="Maroon" title="c1">m</font> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <font color="Maroon" title="c2">n</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Maroon" title="c1">m</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c2">n</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:119"><span class="lab"><font color="Green" title="E98">A1</font></span></a>, <a class="txt" href="#E2:119"><span class="lab"><font color="Green" title="E99">A2</font></span></a>, <a class="ref" href="prepower.html#T94" target="_self" onmouseover="rs('prepower/T94')" onmouseout="rh()">Th94</a></span>;<br/><a NAME="E10:119_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c1">m</font> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <font color="Maroon" title="c2">n</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c1">m</font> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <span class="p1"><a href="int_2.html#K1" title="INT_2:func.1">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">m</font></span>)</span></span><a href="int_2.html#K1" title="INT_2:func.1">.|</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:119"><span class="lab"><font color="Green" title="E98">A1</font></span></a>, <a class="txt" href="#E3:119_1_2"><span class="lab"><font color="Green" title="E102">A7</font></span></a>, <a class="ref" href="nat_d.html#D5" onmouseover="rs('nat_d/D5')" onmouseout="rh()">NAT_D:def 5</a></span>;<br/><span class="kw">hence </span><a NAME="E11:119_1_2"/>
<font color="Maroon" title="c1">m</font> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <font color="Maroon" title="c2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">m</font> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <span class="p1"><a href="int_2.html#K1" title="INT_2:func.1">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">m</font></span>)</span></span><a href="int_2.html#K1" title="INT_2:func.1">.|</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:119_1_2"><span class="lab"><font color="Green" title="E103">A8</font></span></a>, <a class="ref" href="nat_d.html#T5" onmouseover="rs('nat_d/T5')" onmouseout="rh()">NAT_D: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/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

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