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<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="int_1.html#NM1">Integer</a>] means ( ( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 0 implies <font color="Maroon">c<sub>1</sub></font> <a href="int_1.html#K5">div</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 0 ) &amp; ( not <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 0 implies ( ( <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 &amp; <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 implies <font color="Maroon">c<sub>1</sub></font> <a href="int_1.html#K5">div</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="prgcor_1.html#K1" target="_self">idiv1_prg</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> ) &amp; ( (  not <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 or  not <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 ) implies ( ( <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 &amp; <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 implies ( <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="prgcor_1.html#K1" target="_self">idiv1_prg</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> &amp; ( <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> implies <font color="Maroon">c<sub>1</sub></font> <a href="int_1.html#K5">div</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">a<sub>1</sub></font> ) &amp; ( <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>1</sub></font> implies <font color="Maroon">c<sub>1</sub></font> <a href="int_1.html#K5">div</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">a<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 ) ) ) &amp; ( (  not <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 or  not <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 ) implies ( ( <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 &amp; <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 implies ( <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="prgcor_1.html#K1" target="_self">idiv1_prg</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font> &amp; ( <font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>1</sub></font> implies <font color="Maroon">c<sub>1</sub></font> <a href="int_1.html#K5">div</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">a<sub>1</sub></font> ) &amp; ( <font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>1</sub></font> implies <font color="Maroon">c<sub>1</sub></font> <a href="int_1.html#K5">div</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">a<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 ) ) ) &amp; ( (  not <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 or  not <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 ) implies <font color="Maroon">c<sub>1</sub></font> <a href="int_1.html#K5">div</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="prgcor_1.html#K1" target="_self">idiv1_prg</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> ) ) ) ) ) ) ) );<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="14_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:14_1_1_1"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="14_1_1_1_1"><b>suppose </b></a><a NAME="E1:14_1_1_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><b>hence </b><a NAME="E2:14_1_1_1_1"/>
ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="int_1.html#NM1">Integer</a> st <br/>( ( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 0 implies <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> 0 ) &amp; ( not <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 0 implies ( ( <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 &amp; <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 implies <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="prgcor_1.html#K1" target="_self">idiv1_prg</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> ) &amp; ( (  not <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 or  not <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 ) implies ( ( <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 &amp; <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 implies ( <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="prgcor_1.html#K1" target="_self">idiv1_prg</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> &amp; ( <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> implies <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="xcmplx_0.html#K4">-</a> <font color="Olive">b<sub>2</sub></font> ) &amp; ( <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>1</sub></font> implies <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 ) ) ) &amp; ( (  not <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 or  not <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 ) implies ( ( <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 &amp; <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 implies ( <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="prgcor_1.html#K1" target="_self">idiv1_prg</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font> &amp; ( <font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K3">*</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>1</sub></font> implies <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="xcmplx_0.html#K4">-</a> <font color="Olive">b<sub>2</sub></font> ) &amp; ( <font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K3">*</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>1</sub></font> implies <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 ) ) ) &amp; ( (  not <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 or  not <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 ) implies <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="prgcor_1.html#K1" target="_self">idiv1_prg</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> ) ) ) ) ) ) ) )
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="14_1_1_1_2"><b>suppose </b></a><a NAME="E1:14_1_1_1_2"/><i><font color="Green">E12</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="14_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="E1:14_1_1_1_2_1_1"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 or <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="14_1_1_1_2_1_1_1"><b>case </b></a><a NAME="E1:14_1_1_1_2_1_1_1"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 ;<br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_2_1_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="14_1_1_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="E1:14_1_1_1_2_1_1_1_1_1"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 or <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 )
 </span><b>by </b><i><a class="txt" href="prgcor_1.html#E1:14_1_1_1_2"><i><font color="Green">E12</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="14_1_1_1_2_1_1_1_1_1_1"><b>case </b></a><a NAME="E1:14_1_1_1_2_1_1_1_1_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/><div class="add"><a NAME="E2:14_1_1_1_2_1_1_1_1_1_1"/><b>then </b>
<font color="Maroon">S<sub>1</sub></font>[ <a href="prgcor_1.html#K1" target="_self">idiv1_prg</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>]
 <b>by </b><i><a class="txt" href="prgcor_1.html#E1:14_1_1_1_2_1_1_1"><i><font color="Green">E13</font></i></a>, <a class="ref" href="prgcor_1.html#T10" target="_self">Th10</a></i>;<br/><b>hence </b><a NAME="E3:14_1_1_1_2_1_1_1_1_1_1"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="int_1.html#NM1">Integer</a> st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>]
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="14_1_1_1_2_1_1_1_1_1_2"><b>case </b></a><a NAME="E1:14_1_1_1_2_1_1_1_1_1_2"/><i><font color="Green">E14</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0
 ;<br/><div class="add"><a NAME="E2:14_1_1_1_2_1_1_1_1_1_2"/><b>then </b><i><font color="Green">E15</font></i>: 
 <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="ref" href="xreal_1.html#T60">XREAL_1:60</a></i>;<br/><b>then reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>4</sub></font> =  <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font> as   <a href="nat_1.html#NM1">Nat</a> <b>by </b><i><a class="txt" href="prgcor_1.html#E1:14_1_1_1_2_1_1_1"><i><font color="Green">E13</font></i></a>, <a class="ref" href="int_1.html#T16">INT_1:16</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_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="14_1_1_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="E1:14_1_1_1_2_1_1_1_1_1_2_1_1"/>
( <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="prgcor_1.html#K1" target="_self">idiv1_prg</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> or <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="prgcor_1.html#K1" target="_self">idiv1_prg</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>1</sub></font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="14_1_1_1_2_1_1_1_1_1_2_1_1_1"><b>case </b></a><a NAME="E1:14_1_1_1_2_1_1_1_1_1_2_1_1_1"/><i><font color="Green">E16</font></i>: 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="prgcor_1.html#K1" target="_self">idiv1_prg</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><div class="add"><a NAME="E2:14_1_1_1_2_1_1_1_1_1_2_1_1_1"/><i><font color="Green">E17</font></i>: 
 <a href="prgcor_1.html#K1" target="_self">idiv1_prg</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="int_1.html#K5">div</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="prgcor_1.html#E1:14_1_1_1_2_1_1_1"><i><font color="Green">E13</font></i></a>, <a class="txt" href="prgcor_1.html#E2:14_1_1_1_2_1_1_1_1_1_2"><i><font color="Green">E15</font></i></a>, <a class="ref" href="prgcor_1.html#T10" target="_self">Th10</a></i>;<br/><a NAME="E3:14_1_1_1_2_1_1_1_1_1_2_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K2">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K3">div</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="prgcor_1.html#E2:14_1_1_1_2_1_1_1_1_1_2"><i><font color="Green">E15</font></i></a>, <a class="txt" href="prgcor_1.html#E1:14_1_1_1_2_1_1_1_1_1_2_1_1_1"><i><font color="Green">E16</font></i></a>, <a class="ref" href="prgcor_1.html#T11" target="_self">Th11</a></i>;<br/><a NAME="E4:14_1_1_1_2_1_1_1_1_1_2_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="int_1.html#K5">div</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K3">div</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="prgcor_1.html#E1:14_1_1_1_2_1_1_1_1_1_2"><i><font color="Green">E14</font></i></a>, <a class="ref" href="prgcor_1.html#T11" target="_self">Th11</a></i>;<br/><a NAME="E5:14_1_1_1_2_1_1_1_1_1_2_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="int_1.html#K5">div</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><a href="prgcor_1.html#K1" target="_self">idiv1_prg</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="prgcor_1.html#E2:14_1_1_1_2_1_1_1_1_1_2"><i><font color="Green">E15</font></i></a>, <a class="txt" href="prgcor_1.html#E2:14_1_1_1_2_1_1_1_1_1_2_1_1_1"><i><font color="Green">E17</font></i></a>, <a class="ref" href="prgcor_1.html#T11" target="_self">Th11</a></i>;<br/><b>hence </b><a NAME="E6:14_1_1_1_2_1_1_1_1_1_2_1_1_1"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="int_1.html#NM1">Integer</a> st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>]
 <b>by </b><i><a class="txt" href="prgcor_1.html#E1:14_1_1_1_2_1_1_1"><i><font color="Green">E13</font></i></a>, <a class="txt" href="prgcor_1.html#E1:14_1_1_1_2_1_1_1_1_1_2"><i><font color="Green">E14</font></i></a>, <a class="txt" href="prgcor_1.html#E1:14_1_1_1_2_1_1_1_1_1_2_1_1_1"><i><font color="Green">E16</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="14_1_1_1_2_1_1_1_1_1_2_1_1_2"><b>case </b></a><a NAME="E1:14_1_1_1_2_1_1_1_1_1_2_1_1_2"/><i><font color="Green">E16</font></i>: 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="prgcor_1.html#K1" target="_self">idiv1_prg</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><div class="add"><a NAME="E2:14_1_1_1_2_1_1_1_1_1_2_1_1_2"/><i><font color="Green">E17</font></i>: 
 <a href="prgcor_1.html#K1" target="_self">idiv1_prg</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="int_1.html#K5">div</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="prgcor_1.html#E1:14_1_1_1_2_1_1_1"><i><font color="Green">E13</font></i></a>, <a class="txt" href="prgcor_1.html#E2:14_1_1_1_2_1_1_1_1_1_2"><i><font color="Green">E15</font></i></a>, <a class="ref" href="prgcor_1.html#T10" target="_self">Th10</a></i>;<br/><a NAME="E3:14_1_1_1_2_1_1_1_1_1_2_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K2">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K3">div</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="prgcor_1.html#E2:14_1_1_1_2_1_1_1_1_1_2"><i><font color="Green">E15</font></i></a>, <a class="txt" href="prgcor_1.html#E1:14_1_1_1_2_1_1_1_1_1_2_1_1_2"><i><font color="Green">E16</font></i></a>, <a class="ref" href="prgcor_1.html#T11" target="_self">Th11</a></i>;<br/><a NAME="E4:14_1_1_1_2_1_1_1_1_1_2_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="int_1.html#K5">div</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K3">div</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 <b>by </b><i><a class="txt" href="prgcor_1.html#E1:14_1_1_1_2_1_1_1_1_1_2"><i><font color="Green">E14</font></i></a>, <a class="ref" href="prgcor_1.html#T11" target="_self">Th11</a></i>;<br/><a NAME="E5:14_1_1_1_2_1_1_1_1_1_2_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="int_1.html#K5">div</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><a href="prgcor_1.html#K1" target="_self">idiv1_prg</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 <b>by </b><i><a class="txt" href="prgcor_1.html#E2:14_1_1_1_2_1_1_1_1_1_2"><i><font color="Green">E15</font></i></a>, <a class="txt" href="prgcor_1.html#E2:14_1_1_1_2_1_1_1_1_1_2_1_1_2"><i><font color="Green">E17</font></i></a>, <a class="ref" href="prgcor_1.html#T11" target="_self">Th11</a></i>;<br/><b>hence </b><a NAME="E6:14_1_1_1_2_1_1_1_1_1_2_1_1_2"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="int_1.html#NM1">Integer</a> st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>]
 <b>by </b><i><a class="txt" href="prgcor_1.html#E1:14_1_1_1_2_1_1_1"><i><font color="Green">E13</font></i></a>, <a class="txt" href="prgcor_1.html#E1:14_1_1_1_2_1_1_1_1_1_2"><i><font color="Green">E14</font></i></a>, <a class="txt" href="prgcor_1.html#E1:14_1_1_1_2_1_1_1_1_1_2_1_1_2"><i><font color="Green">E16</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E5:14_1_1_1_2_1_1_1_1_1_2"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="int_1.html#NM1">Integer</a> st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>]
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:14_1_1_1_2_1_1_1"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="int_1.html#NM1">Integer</a> st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>]
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="14_1_1_1_2_1_1_2"><b>case </b></a><a NAME="E1:14_1_1_1_2_1_1_2"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0
 ;<br/><div class="add"><a NAME="E2:14_1_1_1_2_1_1_2"/><b>then </b><i><font color="Green">E14</font></i>: 
 <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="ref" href="xreal_1.html#T60">XREAL_1:60</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_2_1_1_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="14_1_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="E1:14_1_1_1_2_1_1_2_1_1"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 or <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 </span><b>by </b><i><a class="txt" href="prgcor_1.html#E1:14_1_1_1_2"><i><font color="Green">E12</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="14_1_1_1_2_1_1_2_1_1_1"><b>case </b></a><a NAME="E1:14_1_1_1_2_1_1_2_1_1_1"/><i><font color="Green">E15</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0
 ;<br/><div class="add"><a NAME="E2:14_1_1_1_2_1_1_2_1_1_1"/><b>then </b><i><font color="Green">E16</font></i>: 
 <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="ref" href="xreal_1.html#T60">XREAL_1:60</a></i>;<br/><font color="Maroon">c<sub>1</sub></font> <a href="int_1.html#K5">div</a> <font color="Maroon">c<sub>2</sub></font> = 
<span class="p1"><a href="int_1.html#K1">[\</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="int_1.html#K1">/]</a></span>
<b>by </b><i><a class="ref" href="int_1.html#D7">INT_1:def 7</a></i>
<br/>.= 
<span class="p1"><a href="int_1.html#K1">[\</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="int_1.html#K1">/]</a></span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T192">XCMPLX_1:192</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="int_1.html#K5">div</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="int_1.html#D7">INT_1:def 7</a></i>
;<br/><a NAME="E4:14_1_1_1_2_1_1_2_1_1_1"/><b>then </b>
<font color="Maroon">S<sub>1</sub></font>[ <a href="prgcor_1.html#K1" target="_self">idiv1_prg</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>]
 <b>by </b><i><a class="txt" href="prgcor_1.html#E1:14_1_1_1_2_1_1_2"><i><font color="Green">E13</font></i></a>, <a class="txt" href="prgcor_1.html#E2:14_1_1_1_2_1_1_2"><i><font color="Green">E14</font></i></a>, <a class="txt" href="prgcor_1.html#E1:14_1_1_1_2_1_1_2_1_1_1"><i><font color="Green">E15</font></i></a>, <a class="txt" href="prgcor_1.html#E2:14_1_1_1_2_1_1_2_1_1_1"><i><font color="Green">E16</font></i></a>, <a class="ref" href="prgcor_1.html#T10" target="_self">Th10</a></i>;<br/><b>hence </b><a NAME="E5:14_1_1_1_2_1_1_2_1_1_1"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="int_1.html#NM1">Integer</a> st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>]
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="14_1_1_1_2_1_1_2_1_1_2"><b>case </b></a><a NAME="E1:14_1_1_1_2_1_1_2_1_1_2"/><i><font color="Green">E15</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">c<sub>3</sub></font> =  <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>2</sub></font> as   <a href="nat_1.html#NM1">Nat</a> <b>by </b><i><a class="txt" href="prgcor_1.html#E2:14_1_1_1_2_1_1_2"><i><font color="Green">E14</font></i></a>, <a class="ref" href="int_1.html#T16">INT_1:16</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_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="14_1_1_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="E1:14_1_1_1_2_1_1_2_1_1_2_1_1"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="prgcor_1.html#K1" target="_self">idiv1_prg</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>1</sub></font> or <font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="prgcor_1.html#K1" target="_self">idiv1_prg</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>1</sub></font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="14_1_1_1_2_1_1_2_1_1_2_1_1_1"><b>case </b></a><a NAME="E1:14_1_1_1_2_1_1_2_1_1_2_1_1_1"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="prgcor_1.html#K1" target="_self">idiv1_prg</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><div class="add"><a NAME="E2:14_1_1_1_2_1_1_2_1_1_2_1_1_1"/><i><font color="Green">E17</font></i>: 
 <a href="prgcor_1.html#K1" target="_self">idiv1_prg</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="int_1.html#K5">div</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="prgcor_1.html#E2:14_1_1_1_2_1_1_2"><i><font color="Green">E14</font></i></a>, <a class="txt" href="prgcor_1.html#E1:14_1_1_1_2_1_1_2_1_1_2"><i><font color="Green">E15</font></i></a>, <a class="ref" href="prgcor_1.html#T10" target="_self">Th10</a></i>;<br/><a NAME="E3:14_1_1_1_2_1_1_2_1_1_2_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K2">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K3">div</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="prgcor_1.html#E1:14_1_1_1_2_1_1_2_1_1_2"><i><font color="Green">E15</font></i></a>, <a class="txt" href="prgcor_1.html#E1:14_1_1_1_2_1_1_2_1_1_2_1_1_1"><i><font color="Green">E16</font></i></a>, <a class="ref" href="prgcor_1.html#T11" target="_self">Th11</a></i>;<br/><a NAME="E4:14_1_1_1_2_1_1_2_1_1_2_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="int_1.html#K5">div</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K3">div</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="prgcor_1.html#E1:14_1_1_1_2_1_1_2"><i><font color="Green">E13</font></i></a>, <a class="txt" href="prgcor_1.html#E1:14_1_1_1_2_1_1_2_1_1_2"><i><font color="Green">E15</font></i></a>, <a class="ref" href="prgcor_1.html#T11" target="_self">Th11</a></i>;<br/><a NAME="E5:14_1_1_1_2_1_1_2_1_1_2_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="int_1.html#K5">div</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><a href="prgcor_1.html#K1" target="_self">idiv1_prg</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="prgcor_1.html#E1:14_1_1_1_2_1_1_2_1_1_2"><i><font color="Green">E15</font></i></a>, <a class="txt" href="prgcor_1.html#E2:14_1_1_1_2_1_1_2_1_1_2_1_1_1"><i><font color="Green">E17</font></i></a>, <a class="ref" href="prgcor_1.html#T11" target="_self">Th11</a></i>;<br/><b>hence </b><a NAME="E6:14_1_1_1_2_1_1_2_1_1_2_1_1_1"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="int_1.html#NM1">Integer</a> st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>]
 <b>by </b><i><a class="txt" href="prgcor_1.html#E1:14_1_1_1_2_1_1_2"><i><font color="Green">E13</font></i></a>, <a class="txt" href="prgcor_1.html#E1:14_1_1_1_2_1_1_2_1_1_2"><i><font color="Green">E15</font></i></a>, <a class="txt" href="prgcor_1.html#E1:14_1_1_1_2_1_1_2_1_1_2_1_1_1"><i><font color="Green">E16</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="14_1_1_1_2_1_1_2_1_1_2_1_1_2"><b>case </b></a><a NAME="E1:14_1_1_1_2_1_1_2_1_1_2_1_1_2"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="prgcor_1.html#K1" target="_self">idiv1_prg</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><div class="add"><a NAME="E2:14_1_1_1_2_1_1_2_1_1_2_1_1_2"/><i><font color="Green">E17</font></i>: 
 <a href="prgcor_1.html#K1" target="_self">idiv1_prg</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="int_1.html#K5">div</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="prgcor_1.html#E2:14_1_1_1_2_1_1_2"><i><font color="Green">E14</font></i></a>, <a class="txt" href="prgcor_1.html#E1:14_1_1_1_2_1_1_2_1_1_2"><i><font color="Green">E15</font></i></a>, <a class="ref" href="prgcor_1.html#T10" target="_self">Th10</a></i>;<br/><a NAME="E3:14_1_1_1_2_1_1_2_1_1_2_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K2">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K3">div</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="prgcor_1.html#E1:14_1_1_1_2_1_1_2_1_1_2"><i><font color="Green">E15</font></i></a>, <a class="txt" href="prgcor_1.html#E1:14_1_1_1_2_1_1_2_1_1_2_1_1_2"><i><font color="Green">E16</font></i></a>, <a class="ref" href="prgcor_1.html#T11" target="_self">Th11</a></i>;<br/><a NAME="E4:14_1_1_1_2_1_1_2_1_1_2_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="int_1.html#K5">div</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K3">div</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 <b>by </b><i><a class="txt" href="prgcor_1.html#E1:14_1_1_1_2_1_1_2"><i><font color="Green">E13</font></i></a>, <a class="txt" href="prgcor_1.html#E1:14_1_1_1_2_1_1_2_1_1_2"><i><font color="Green">E15</font></i></a>, <a class="ref" href="prgcor_1.html#T11" target="_self">Th11</a></i>;<br/><a NAME="E5:14_1_1_1_2_1_1_2_1_1_2_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="int_1.html#K5">div</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><a href="prgcor_1.html#K1" target="_self">idiv1_prg</a> <span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 <b>by </b><i><a class="txt" href="prgcor_1.html#E1:14_1_1_1_2_1_1_2_1_1_2"><i><font color="Green">E15</font></i></a>, <a class="txt" href="prgcor_1.html#E2:14_1_1_1_2_1_1_2_1_1_2_1_1_2"><i><font color="Green">E17</font></i></a>, <a class="ref" href="prgcor_1.html#T11" target="_self">Th11</a></i>;<br/><b>hence </b><a NAME="E6:14_1_1_1_2_1_1_2_1_1_2_1_1_2"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="int_1.html#NM1">Integer</a> st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>]
 <b>by </b><i><a class="txt" href="prgcor_1.html#E1:14_1_1_1_2_1_1_2"><i><font color="Green">E13</font></i></a>, <a class="txt" href="prgcor_1.html#E1:14_1_1_1_2_1_1_2_1_1_2"><i><font color="Green">E15</font></i></a>, <a class="txt" href="prgcor_1.html#E1:14_1_1_1_2_1_1_2_1_1_2_1_1_2"><i><font color="Green">E16</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E4:14_1_1_1_2_1_1_2_1_1_2"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="int_1.html#NM1">Integer</a> st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>]
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E4:14_1_1_1_2_1_1_2"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="int_1.html#NM1">Integer</a> st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>]
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:14_1_1_1_2"/>
ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="int_1.html#NM1">Integer</a> st <br/>( ( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 0 implies <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> 0 ) &amp; ( not <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 0 implies ( ( <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 &amp; <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 implies <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="prgcor_1.html#K1" target="_self">idiv1_prg</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> ) &amp; ( (  not <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 or  not <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 ) implies ( ( <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 &amp; <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 implies ( <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="prgcor_1.html#K1" target="_self">idiv1_prg</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> &amp; ( <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> implies <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="xcmplx_0.html#K4">-</a> <font color="Olive">b<sub>2</sub></font> ) &amp; ( <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>1</sub></font> implies <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 ) ) ) &amp; ( (  not <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 or  not <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 ) implies ( ( <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 &amp; <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 implies ( <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="prgcor_1.html#K1" target="_self">idiv1_prg</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font> &amp; ( <font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K3">*</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>1</sub></font> implies <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="xcmplx_0.html#K4">-</a> <font color="Olive">b<sub>2</sub></font> ) &amp; ( <font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K3">*</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>1</sub></font> implies <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 ) ) ) &amp; ( (  not <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 or  not <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 ) implies <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="prgcor_1.html#K1" target="_self">idiv1_prg</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> ) ) ) ) ) ) ) )
 ;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
