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<b>let </b><font color="Maroon" title="c1">n</font>, <font color="Maroon" title="c2">m</font> be   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:15_1"/>
( <font color="Maroon" title="c2">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 or <font color="Maroon" title="c2">m</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_1_1"><b>suppose </b></a><a NAME="E1:15_1_1"/><i><font color="Green" title="E13">A1</font></i>: 
<font color="Maroon" title="c2">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 ;<br/><div class="add"><a NAME="E2:15_1_1"/><b>then </b>
 <a href="prgcor_1.html#K2" title="PRGCOR_1:func.2">idiv_prg</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 <b>by </b><i><a class="ref" href="prgcor_1.html#D2" target="_self" title="PRGCOR_1:def.2">Def2</a></i>;<br/><b>hence </b><a NAME="E3:15_1_1"/>
 <a href="prgcor_1.html#K2" title="PRGCOR_1:func.2">idiv_prg</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <font color="Maroon" title="c2">m</font>
 <b>by </b><i><a class="txt" href="prgcor_1.html#E1:15_1_1"><i><font color="Green" title="E13">A1</font></i></a>, <a class="ref" href="int_1.html#T75" title="INT_1:th.75">INT_1:75</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_1_2"><b>suppose </b></a><a NAME="E1:15_1_2"/><i><font color="Green" title="E13">A2</font></i>: 
<font color="Maroon" title="c2">m</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0
 ;<br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:15_1_2_1_1"/>
( <font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 0 or <font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_1_2_1_1_1"><b>case </b></a><a NAME="E1:15_1_2_1_1_1"/><i><font color="Green" title="E14">A3</font></i>: 
<font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 0
 ;<br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_2_1_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_1_2_1_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:15_1_2_1_1_1_1_1"/>
( <font color="Maroon" title="c2">m</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0 or <font color="Maroon" title="c2">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 0 )
 </span><b>by </b><i><a class="txt" href="prgcor_1.html#E1:15_1_2"><i><font color="Green" title="E13">A2</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_1_2_1_1_1_1_1_1"><b>case </b></a><a NAME="E1:15_1_2_1_1_1_1_1_1"/><i><font color="Green" title="E15">A4</font></i>: 
<font color="Maroon" title="c2">m</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 ;<br/><div class="add"><b>hence </b> <a href="prgcor_1.html#K2" title="PRGCOR_1:func.2">idiv_prg</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font> = 
 <a href="prgcor_1.html#K1" title="PRGCOR_1:func.1">idiv1_prg</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font>
<b>by </b><i><a class="txt" href="prgcor_1.html#E1:15_1_2_1_1_1"><i><font color="Green" title="E14">A3</font></i></a>, <a class="ref" href="prgcor_1.html#D2" target="_self" title="PRGCOR_1:def.2">Def2</a></i>
<br/>.= 
<font color="Maroon" title="c1">n</font> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <font color="Maroon" title="c2">m</font>
<b>by </b><i><a class="txt" href="prgcor_1.html#E1:15_1_2_1_1_1"><i><font color="Green" title="E14">A3</font></i></a>, <a class="txt" href="prgcor_1.html#E1:15_1_2_1_1_1_1_1_1"><i><font color="Green" title="E15">A4</font></i></a>, <a class="ref" href="prgcor_1.html#T10" target="_self" title="PRGCOR_1:th.10">Th10</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_1_2_1_1_1_1_1_2"><b>case </b></a><a NAME="E1:15_1_2_1_1_1_1_1_2"/><i><font color="Green" title="E15">A5</font></i>: 
<font color="Maroon" title="c2">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 0
 ;<br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_2_1_1_1_1_1_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_1_2_1_1_1_1_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:15_1_2_1_1_1_1_1_2_1_1"/>
( <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c2">m</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="prgcor_1.html#K1" title="PRGCOR_1:func.1">idiv1_prg</a> <font color="Maroon" title="c1">n</font>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c2">m</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> or <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c2">m</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="prgcor_1.html#K1" title="PRGCOR_1:func.1">idiv1_prg</a> <font color="Maroon" title="c1">n</font>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c2">m</font></span>)</span></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c1">n</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_1_2_1_1_1_1_1_2_1_1_1"><b>case </b></a><a NAME="E1:15_1_2_1_1_1_1_1_2_1_1_1"/><i><font color="Green" title="E16">A6</font></i>: 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c2">m</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="prgcor_1.html#K1" title="PRGCOR_1:func.1">idiv1_prg</a> <font color="Maroon" title="c1">n</font>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c2">m</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font>
 ;<br/><div class="add"><a NAME="E2:15_1_2_1_1_1_1_1_2_1_1_1"/><i><font color="Green" title="E17">A7</font></i>: 
 <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c2">m</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 <b>by </b><i><a class="txt" href="prgcor_1.html#E1:15_1_2_1_1_1_1_1_2"><i><font color="Green" title="E15">A5</font></i></a>, <a class="ref" href="xreal_1.html#T60" title="XREAL_1:th.60">XREAL_1:60</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c3">m2</font> =  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c2">m</font>, <font color="Maroon" title="c4">n2</font> = <font color="Maroon" title="c1">n</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <b>by </b><i><a class="txt" href="prgcor_1.html#E1:15_1_2_1_1_1"><i><font color="Green" title="E14">A3</font></i></a>, <a class="ref" href="int_1.html#T16" title="INT_1:th.16">INT_1:16</a></i>;<br/><a NAME="E4:15_1_2_1_1_1_1_1_2_1_1_1"/><i><font color="Green" title="E18">A8</font></i>: 
 <a href="prgcor_1.html#K2" title="PRGCOR_1:func.2">idiv_prg</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p1">(<span class="default"><a href="prgcor_1.html#K1" title="PRGCOR_1:func.1">idiv1_prg</a> <font color="Maroon" title="c1">n</font>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c2">m</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="prgcor_1.html#E1:15_1_2_1_1_1"><i><font color="Green" title="E14">A3</font></i></a>, <a class="txt" href="prgcor_1.html#E1:15_1_2_1_1_1_1_1_2"><i><font color="Green" title="E15">A5</font></i></a>, <a class="txt" href="prgcor_1.html#E1:15_1_2_1_1_1_1_1_2_1_1_1"><i><font color="Green" title="E16">A6</font></i></a>, <a class="ref" href="prgcor_1.html#D2" target="_self" title="PRGCOR_1:def.2">Def2</a></i>;<br/><a NAME="E5:15_1_2_1_1_1_1_1_2_1_1_1"/>
 <a href="prgcor_1.html#K1" title="PRGCOR_1:func.1">idiv1_prg</a> <font color="Maroon" title="c1">n</font>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c2">m</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">n2</font> <a href="nat_d.html#K3" title="NAT_D:func.3">div</a> <font color="Maroon" title="c3">m2</font>
 <b>by </b><i><a class="txt" href="prgcor_1.html#E2:15_1_2_1_1_1_1_1_2_1_1_1"><i><font color="Green" title="E17">A7</font></i></a>, <a class="ref" href="prgcor_1.html#T9" target="_self" title="PRGCOR_1:th.9">Th9</a></i>;<br/><b>then </b><font color="Maroon" title="c1">n</font> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <font color="Maroon" title="c2">m</font> = 
 <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">n2</font> <a href="nat_d.html#K3" title="NAT_D:func.3">div</a> <font color="Maroon" title="c3">m2</font></span>)</span>
<b>by </b><i><a class="txt" href="prgcor_1.html#E1:15_1_2_1_1_1_1_1_2"><i><font color="Green" title="E15">A5</font></i></a>, <a class="txt" href="prgcor_1.html#E1:15_1_2_1_1_1_1_1_2_1_1_1"><i><font color="Green" title="E16">A6</font></i></a>, <a class="ref" href="prgcor_1.html#T11" target="_self" title="PRGCOR_1:th.11">Th11</a></i>
<br/>.= 
 <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c2">m</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="prgcor_1.html#E2:15_1_2_1_1_1_1_1_2_1_1_1"><i><font color="Green" title="E17">A7</font></i></a>, <a class="ref" href="prgcor_1.html#T11" target="_self" title="PRGCOR_1:th.11">Th11</a></i>
;<br/><b>hence </b><a NAME="E7:15_1_2_1_1_1_1_1_2_1_1_1"/>
 <a href="prgcor_1.html#K2" title="PRGCOR_1:func.2">idiv_prg</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <font color="Maroon" title="c2">m</font>
 <b>by </b><i><a class="txt" href="prgcor_1.html#E1:15_1_2_1_1_1"><i><font color="Green" title="E14">A3</font></i></a>, <a class="txt" href="prgcor_1.html#E2:15_1_2_1_1_1_1_1_2_1_1_1"><i><font color="Green" title="E17">A7</font></i></a>, <a class="txt" href="prgcor_1.html#E4:15_1_2_1_1_1_1_1_2_1_1_1"><i><font color="Green" title="E18">A8</font></i></a>, <a class="ref" href="prgcor_1.html#T10" target="_self" title="PRGCOR_1:th.10">Th10</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_1_2_1_1_1_1_1_2_1_1_2"><b>case </b></a><a NAME="E1:15_1_2_1_1_1_1_1_2_1_1_2"/><i><font color="Green" title="E16">A9</font></i>: 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c2">m</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="prgcor_1.html#K1" title="PRGCOR_1:func.1">idiv1_prg</a> <font color="Maroon" title="c1">n</font>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c2">m</font></span>)</span></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c1">n</font>
 ;<br/><div class="add"><a NAME="E2:15_1_2_1_1_1_1_1_2_1_1_2"/><i><font color="Green" title="E17">A10</font></i>: 
 <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c2">m</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 <b>by </b><i><a class="txt" href="prgcor_1.html#E1:15_1_2_1_1_1_1_1_2"><i><font color="Green" title="E15">A5</font></i></a>, <a class="ref" href="xreal_1.html#T60" title="XREAL_1:th.60">XREAL_1:60</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c3">m2</font> =  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c2">m</font>, <font color="Maroon" title="c4">n2</font> = <font color="Maroon" title="c1">n</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <b>by </b><i><a class="txt" href="prgcor_1.html#E1:15_1_2_1_1_1"><i><font color="Green" title="E14">A3</font></i></a>, <a class="ref" href="int_1.html#T16" title="INT_1:th.16">INT_1:16</a></i>;<br/><a NAME="E4:15_1_2_1_1_1_1_1_2_1_1_2"/><i><font color="Green" title="E18">A11</font></i>: 
 <a href="prgcor_1.html#K2" title="PRGCOR_1:func.2">idiv_prg</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p2">(<span class="default"><a href="prgcor_1.html#K1" title="PRGCOR_1:func.1">idiv1_prg</a> <font color="Maroon" title="c1">n</font>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c2">m</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
 <b>by </b><i><a class="txt" href="prgcor_1.html#E1:15_1_2_1_1_1"><i><font color="Green" title="E14">A3</font></i></a>, <a class="txt" href="prgcor_1.html#E1:15_1_2_1_1_1_1_1_2"><i><font color="Green" title="E15">A5</font></i></a>, <a class="txt" href="prgcor_1.html#E1:15_1_2_1_1_1_1_1_2_1_1_2"><i><font color="Green" title="E16">A9</font></i></a>, <a class="ref" href="prgcor_1.html#D2" target="_self" title="PRGCOR_1:def.2">Def2</a></i>;<br/><a NAME="E5:15_1_2_1_1_1_1_1_2_1_1_2"/>
 <a href="prgcor_1.html#K1" title="PRGCOR_1:func.1">idiv1_prg</a> <font color="Maroon" title="c1">n</font>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c2">m</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">n2</font> <a href="nat_d.html#K3" title="NAT_D:func.3">div</a> <font color="Maroon" title="c3">m2</font>
 <b>by </b><i><a class="txt" href="prgcor_1.html#E2:15_1_2_1_1_1_1_1_2_1_1_2"><i><font color="Green" title="E17">A10</font></i></a>, <a class="ref" href="prgcor_1.html#T9" target="_self" title="PRGCOR_1:th.9">Th9</a></i>;<br/><b>then </b><font color="Maroon" title="c1">n</font> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <font color="Maroon" title="c2">m</font> = 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">n2</font> <a href="nat_d.html#K3" title="NAT_D:func.3">div</a> <font color="Maroon" title="c3">m2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
<b>by </b><i><a class="txt" href="prgcor_1.html#E1:15_1_2_1_1_1_1_1_2"><i><font color="Green" title="E15">A5</font></i></a>, <a class="txt" href="prgcor_1.html#E1:15_1_2_1_1_1_1_1_2_1_1_2"><i><font color="Green" title="E16">A9</font></i></a>, <a class="ref" href="prgcor_1.html#T11" target="_self" title="PRGCOR_1:th.11">Th11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c2">m</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
<b>by </b><i><a class="txt" href="prgcor_1.html#E2:15_1_2_1_1_1_1_1_2_1_1_2"><i><font color="Green" title="E17">A10</font></i></a>, <a class="ref" href="prgcor_1.html#T11" target="_self" title="PRGCOR_1:th.11">Th11</a></i>
;<br/><b>hence </b><a NAME="E7:15_1_2_1_1_1_1_1_2_1_1_2"/>
 <a href="prgcor_1.html#K2" title="PRGCOR_1:func.2">idiv_prg</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <font color="Maroon" title="c2">m</font>
 <b>by </b><i><a class="txt" href="prgcor_1.html#E1:15_1_2_1_1_1"><i><font color="Green" title="E14">A3</font></i></a>, <a class="txt" href="prgcor_1.html#E2:15_1_2_1_1_1_1_1_2_1_1_2"><i><font color="Green" title="E17">A10</font></i></a>, <a class="txt" href="prgcor_1.html#E4:15_1_2_1_1_1_1_1_2_1_1_2"><i><font color="Green" title="E18">A11</font></i></a>, <a class="ref" href="prgcor_1.html#T10" target="_self" title="PRGCOR_1:th.10">Th10</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:15_1_2_1_1_1_1_1_2"/>
 <a href="prgcor_1.html#K2" title="PRGCOR_1:func.2">idiv_prg</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <font color="Maroon" title="c2">m</font>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:15_1_2_1_1_1"/>
 <a href="prgcor_1.html#K2" title="PRGCOR_1:func.2">idiv_prg</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <font color="Maroon" title="c2">m</font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_1_2_1_1_2"><b>case </b></a><a NAME="E1:15_1_2_1_1_2"/><i><font color="Green" title="E14">A12</font></i>: 
<font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 0
 ;<br/><div class="add"><a NAME="E2:15_1_2_1_1_2"/><b>then </b><i><font color="Green" title="E15">A13</font></i>: 
 <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 <b>by </b><i><a class="ref" href="xreal_1.html#T60" title="XREAL_1:th.60">XREAL_1:60</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_2_1_1_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_1_2_1_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:15_1_2_1_1_2_1_1"/>
( <font color="Maroon" title="c2">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 0 or <font color="Maroon" title="c2">m</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0 )
 </span><b>by </b><i><a class="txt" href="prgcor_1.html#E1:15_1_2"><i><font color="Green" title="E13">A2</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_1_2_1_1_2_1_1_1"><b>case </b></a><a NAME="E1:15_1_2_1_1_2_1_1_1"/><i><font color="Green" title="E16">A14</font></i>: 
<font color="Maroon" title="c2">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 0
 ;<br/><div class="add"><a NAME="E2:15_1_2_1_1_2_1_1_1"/><b>then </b><i><font color="Green" title="E17">A15</font></i>: 
 <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c2">m</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 <b>by </b><i><a class="ref" href="xreal_1.html#T60" title="XREAL_1:th.60">XREAL_1:60</a></i>;<br/><i><font color="Green" title="E18">A16</font></i>:  <a href="prgcor_1.html#K2" title="PRGCOR_1:func.2">idiv_prg</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font> = 
 <a href="prgcor_1.html#K1" title="PRGCOR_1:func.1">idiv1_prg</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c1">n</font></span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c2">m</font></span>)</span>
<b>by </b><i><a class="txt" href="prgcor_1.html#E1:15_1_2_1_1_2"><i><font color="Green" title="E14">A12</font></i></a>, <a class="txt" href="prgcor_1.html#E1:15_1_2_1_1_2_1_1_1"><i><font color="Green" title="E16">A14</font></i></a>, <a class="ref" href="prgcor_1.html#D2" target="_self" title="PRGCOR_1:def.2">Def2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c2">m</font></span>)</span>
<b>by </b><i><a class="txt" href="prgcor_1.html#E2:15_1_2_1_1_2"><i><font color="Green" title="E15">A13</font></i></a>, <a class="txt" href="prgcor_1.html#E2:15_1_2_1_1_2_1_1_1"><i><font color="Green" title="E17">A15</font></i></a>, <a class="ref" href="prgcor_1.html#T10" target="_self" title="PRGCOR_1:th.10">Th10</a></i>
;<br/><font color="Maroon" title="c1">n</font> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <font color="Maroon" title="c2">m</font> = 
<span class="p1"><a href="int_1.html#K1" title="INT_1:func.1">[\</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c2">m</font></span>)</span></span><a href="int_1.html#K1" title="INT_1:func.1">/]</a></span>
<b>by </b><i><a class="ref" href="int_1.html#D7" title="INT_1:def.7">INT_1:def 7</a></i>
<br/>.= 
<span class="p1"><a href="int_1.html#K1" title="INT_1:func.1">[\</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c2">m</font></span>)</span></span>)</span></span><a href="int_1.html#K1" title="INT_1:func.1">/]</a></span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T192" title="XCMPLX_1:th.192">XCMPLX_1:192</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c2">m</font></span>)</span>
<b>by </b><i><a class="ref" href="int_1.html#D7" title="INT_1:def.7">INT_1:def 7</a></i>
;<br/><b>hence </b><a NAME="E5:15_1_2_1_1_2_1_1_1"/>
 <a href="prgcor_1.html#K2" title="PRGCOR_1:func.2">idiv_prg</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <font color="Maroon" title="c2">m</font>
 <b>by </b><i><a class="txt" href="prgcor_1.html#E3:15_1_2_1_1_2_1_1_1"><i><font color="Green" title="E18">A16</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_1_2_1_1_2_1_1_2"><b>case </b></a><a NAME="E1:15_1_2_1_1_2_1_1_2"/><i><font color="Green" title="E16">A17</font></i>: 
<font color="Maroon" title="c2">m</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 ;<br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_2_1_1_2_1_1_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_1_2_1_1_2_1_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:15_1_2_1_1_2_1_1_2_1_1"/>
( <font color="Maroon" title="c2">m</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="prgcor_1.html#K1" title="PRGCOR_1:func.1">idiv1_prg</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">m</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c1">n</font> or <font color="Maroon" title="c2">m</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="prgcor_1.html#K1" title="PRGCOR_1:func.1">idiv1_prg</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">m</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c1">n</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_1_2_1_1_2_1_1_2_1_1_1"><b>case </b></a><a NAME="E1:15_1_2_1_1_2_1_1_2_1_1_1"/><i><font color="Green" title="E17">A18</font></i>: 
<font color="Maroon" title="c2">m</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="prgcor_1.html#K1" title="PRGCOR_1:func.1">idiv1_prg</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">m</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c1">n</font>
 ;<br/><div class="add"><b>reconsider </b><font color="Maroon" title="c3">m2</font> = <font color="Maroon" title="c2">m</font>, <font color="Maroon" title="c4">n2</font> =  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c1">n</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <b>by </b><i><a class="txt" href="prgcor_1.html#E2:15_1_2_1_1_2"><i><font color="Green" title="E15">A13</font></i></a>, <a class="txt" href="prgcor_1.html#E1:15_1_2_1_1_2_1_1_2"><i><font color="Green" title="E16">A17</font></i></a>, <a class="ref" href="int_1.html#T16" title="INT_1:th.16">INT_1:16</a></i>;<br/><a NAME="E3:15_1_2_1_1_2_1_1_2_1_1_1"/><i><font color="Green" title="E18">A19</font></i>: 
 <a href="prgcor_1.html#K2" title="PRGCOR_1:func.2">idiv_prg</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p1">(<span class="default"><a href="prgcor_1.html#K1" title="PRGCOR_1:func.1">idiv1_prg</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">m</font></span>)</span>
 <b>by </b><i><a class="txt" href="prgcor_1.html#E1:15_1_2_1_1_2"><i><font color="Green" title="E14">A12</font></i></a>, <a class="txt" href="prgcor_1.html#E1:15_1_2_1_1_2_1_1_2"><i><font color="Green" title="E16">A17</font></i></a>, <a class="txt" href="prgcor_1.html#E1:15_1_2_1_1_2_1_1_2_1_1_1"><i><font color="Green" title="E17">A18</font></i></a>, <a class="ref" href="prgcor_1.html#D2" target="_self" title="PRGCOR_1:def.2">Def2</a></i>;<br/><a NAME="E4:15_1_2_1_1_2_1_1_2_1_1_1"/>
 <a href="prgcor_1.html#K1" title="PRGCOR_1:func.1">idiv1_prg</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">n2</font> <a href="nat_d.html#K3" title="NAT_D:func.3">div</a> <font color="Maroon" title="c3">m2</font>
 <b>by </b><i><a class="txt" href="prgcor_1.html#E1:15_1_2_1_1_2_1_1_2"><i><font color="Green" title="E16">A17</font></i></a>, <a class="ref" href="prgcor_1.html#T9" target="_self" title="PRGCOR_1:th.9">Th9</a></i>;<br/><b>then </b><font color="Maroon" title="c1">n</font> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <font color="Maroon" title="c2">m</font> = 
 <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">n2</font> <a href="nat_d.html#K3" title="NAT_D:func.3">div</a> <font color="Maroon" title="c3">m2</font></span>)</span>
<b>by </b><i><a class="txt" href="prgcor_1.html#E1:15_1_2_1_1_2"><i><font color="Green" title="E14">A12</font></i></a>, <a class="txt" href="prgcor_1.html#E1:15_1_2_1_1_2_1_1_2"><i><font color="Green" title="E16">A17</font></i></a>, <a class="txt" href="prgcor_1.html#E1:15_1_2_1_1_2_1_1_2_1_1_1"><i><font color="Green" title="E17">A18</font></i></a>, <a class="ref" href="prgcor_1.html#T11" target="_self" title="PRGCOR_1:th.11">Th11</a></i>
<br/>.= 
 <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <font color="Maroon" title="c2">m</font></span>)</span>
<b>by </b><i><a class="txt" href="prgcor_1.html#E1:15_1_2_1_1_2_1_1_2"><i><font color="Green" title="E16">A17</font></i></a>, <a class="ref" href="prgcor_1.html#T11" target="_self" title="PRGCOR_1:th.11">Th11</a></i>
;<br/><b>hence </b><a NAME="E6:15_1_2_1_1_2_1_1_2_1_1_1"/>
 <a href="prgcor_1.html#K2" title="PRGCOR_1:func.2">idiv_prg</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <font color="Maroon" title="c2">m</font>
 <b>by </b><i><a class="txt" href="prgcor_1.html#E2:15_1_2_1_1_2"><i><font color="Green" title="E15">A13</font></i></a>, <a class="txt" href="prgcor_1.html#E1:15_1_2_1_1_2_1_1_2"><i><font color="Green" title="E16">A17</font></i></a>, <a class="txt" href="prgcor_1.html#E3:15_1_2_1_1_2_1_1_2_1_1_1"><i><font color="Green" title="E18">A19</font></i></a>, <a class="ref" href="prgcor_1.html#T10" target="_self" title="PRGCOR_1:th.10">Th10</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_1_2_1_1_2_1_1_2_1_1_2"><b>case </b></a><a NAME="E1:15_1_2_1_1_2_1_1_2_1_1_2"/><i><font color="Green" title="E17">A20</font></i>: 
<font color="Maroon" title="c2">m</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="prgcor_1.html#K1" title="PRGCOR_1:func.1">idiv1_prg</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">m</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c1">n</font>
 ;<br/><div class="add"><b>reconsider </b><font color="Maroon" title="c3">m2</font> = <font color="Maroon" title="c2">m</font>, <font color="Maroon" title="c4">n2</font> =  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c1">n</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <b>by </b><i><a class="txt" href="prgcor_1.html#E2:15_1_2_1_1_2"><i><font color="Green" title="E15">A13</font></i></a>, <a class="txt" href="prgcor_1.html#E1:15_1_2_1_1_2_1_1_2"><i><font color="Green" title="E16">A17</font></i></a>, <a class="ref" href="int_1.html#T16" title="INT_1:th.16">INT_1:16</a></i>;<br/><a NAME="E3:15_1_2_1_1_2_1_1_2_1_1_2"/><i><font color="Green" title="E18">A21</font></i>: 
 <a href="prgcor_1.html#K2" title="PRGCOR_1:func.2">idiv_prg</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p2">(<span class="default"><a href="prgcor_1.html#K1" title="PRGCOR_1:func.1">idiv1_prg</a> <span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">m</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
 <b>by </b><i><a class="txt" href="prgcor_1.html#E1:15_1_2_1_1_2"><i><font color="Green" title="E14">A12</font></i></a>, <a class="txt" href="prgcor_1.html#E1:15_1_2_1_1_2_1_1_2"><i><font color="Green" title="E16">A17</font></i></a>, <a class="txt" href="prgcor_1.html#E1:15_1_2_1_1_2_1_1_2_1_1_2"><i><font color="Green" title="E17">A20</font></i></a>, <a class="ref" href="prgcor_1.html#D2" target="_self" title="PRGCOR_1:def.2">Def2</a></i>;<br/><a NAME="E4:15_1_2_1_1_2_1_1_2_1_1_2"/>
 <a href="prgcor_1.html#K1" title="PRGCOR_1:func.1">idiv1_prg</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">n2</font> <a href="nat_d.html#K3" title="NAT_D:func.3">div</a> <font color="Maroon" title="c3">m2</font>
 <b>by </b><i><a class="txt" href="prgcor_1.html#E1:15_1_2_1_1_2_1_1_2"><i><font color="Green" title="E16">A17</font></i></a>, <a class="ref" href="prgcor_1.html#T9" target="_self" title="PRGCOR_1:th.9">Th9</a></i>;<br/><b>then </b><font color="Maroon" title="c1">n</font> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <font color="Maroon" title="c2">m</font> = 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">n2</font> <a href="nat_d.html#K3" title="NAT_D:func.3">div</a> <font color="Maroon" title="c3">m2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
<b>by </b><i><a class="txt" href="prgcor_1.html#E1:15_1_2_1_1_2"><i><font color="Green" title="E14">A12</font></i></a>, <a class="txt" href="prgcor_1.html#E1:15_1_2_1_1_2_1_1_2"><i><font color="Green" title="E16">A17</font></i></a>, <a class="txt" href="prgcor_1.html#E1:15_1_2_1_1_2_1_1_2_1_1_2"><i><font color="Green" title="E17">A20</font></i></a>, <a class="ref" href="prgcor_1.html#T11" target="_self" title="PRGCOR_1:th.11">Th11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <font color="Maroon" title="c2">m</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
<b>by </b><i><a class="txt" href="prgcor_1.html#E1:15_1_2_1_1_2_1_1_2"><i><font color="Green" title="E16">A17</font></i></a>, <a class="ref" href="prgcor_1.html#T11" target="_self" title="PRGCOR_1:th.11">Th11</a></i>
;<br/><b>hence </b><a NAME="E6:15_1_2_1_1_2_1_1_2_1_1_2"/>
 <a href="prgcor_1.html#K2" title="PRGCOR_1:func.2">idiv_prg</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <font color="Maroon" title="c2">m</font>
 <b>by </b><i><a class="txt" href="prgcor_1.html#E2:15_1_2_1_1_2"><i><font color="Green" title="E15">A13</font></i></a>, <a class="txt" href="prgcor_1.html#E1:15_1_2_1_1_2_1_1_2"><i><font color="Green" title="E16">A17</font></i></a>, <a class="txt" href="prgcor_1.html#E3:15_1_2_1_1_2_1_1_2_1_1_2"><i><font color="Green" title="E18">A21</font></i></a>, <a class="ref" href="prgcor_1.html#T10" target="_self" title="PRGCOR_1:th.10">Th10</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:15_1_2_1_1_2_1_1_2"/>
 <a href="prgcor_1.html#K2" title="PRGCOR_1:func.2">idiv_prg</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <font color="Maroon" title="c2">m</font>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E4:15_1_2_1_1_2"/>
 <a href="prgcor_1.html#K2" title="PRGCOR_1:func.2">idiv_prg</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <font color="Maroon" title="c2">m</font>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:15_1_2"/>
 <a href="prgcor_1.html#K2" title="PRGCOR_1:func.2">idiv_prg</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <font color="Maroon" title="c2">m</font>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
