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<b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a> ;<br/>

<b>assume </b><a NAME="E1:21"/><i><font color="Green" title="E15">A1</font></i>: 
<font color="Maroon" title="c3">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a> 
 ;<br/>

<b>consider </b><font color="Maroon" title="c4">d</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a> <b> such that </b><br/><a NAME="E3:21"/><i><font color="Green" title="E16">A2</font></i>: 
<font color="Maroon" title="c4">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> <a href="int_3.html#K4" title="INT_3:func.4">div</a> <font color="Maroon" title="c3">b</font>
 ;<br/>
<b>consider </b><font color="Maroon" title="c5">c</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a> <b> such that </b><br/><a NAME="E5:21"/><i><font color="Green" title="E17">A3</font></i>: 
<font color="Maroon" title="c5">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> <a href="int_3.html#K5" title="INT_3:func.5">mod</a> <font color="Maroon" title="c3">b</font>
 ;<br/>
<b>consider </b><font color="Maroon" title="c6">r</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a> <b> such that </b><br/><a NAME="E7:21"/><i><font color="Green" title="E18">A4</font></i>: 
( <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">d</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c6">r</font> &amp;  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">r</font> &amp; <font color="Maroon" title="c6">r</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="int_3.html#K2" title="INT_3:func.2">abs</a> <font color="Maroon" title="c3">b</font> )
 <b>by </b><i><a class="txt" href="int_3.html#E1:21"><i><font color="Green" title="E15">A1</font></i></a>, <a class="txt" href="int_3.html#E3:21"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="int_3.html#D7" target="_self" title="INT_3:def.7">Def7</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c7">q</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a> <b> such that </b><br/><a NAME="E9:21"/><i><font color="Green" title="E19">A5</font></i>: 
( <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">q</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c5">c</font> &amp;  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c5">c</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="int_3.html#K2" title="INT_3:func.2">abs</a> <font color="Maroon" title="c3">b</font> )
 <b>by </b><i><a class="txt" href="int_3.html#E1:21"><i><font color="Green" title="E15">A1</font></i></a>, <a class="txt" href="int_3.html#E5:21"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="int_3.html#D8" target="_self" title="INT_3:def.8">Def8</a></i>;<br/>
<b>thus </b><a NAME="E10:21"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="int_3.html#K4" title="INT_3:func.4">div</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="int_3.html#K5" title="INT_3:func.5">mod</a> <font color="Maroon" title="c3">b</font></span>)</span>
 <b>by </b><i><a class="txt" href="int_3.html#E1:21"><i><font color="Green" title="E15">A1</font></i></a>, <a class="txt" href="int_3.html#E3:21"><i><font color="Green" title="E16">A2</font></i></a>, <a class="txt" href="int_3.html#E5:21"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="int_3.html#E7:21"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="int_3.html#E9:21"><i><font color="Green" title="E19">A5</font></i></a>, <a class="ref" href="int_3.html#T2" target="_self" title="INT_3:th.2">Th2</a></i>;<br/>


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