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<div class="add">

<b>let </b><font color="Maroon" title="c1">R</font> be   <a href="gcd_1.html#NM3" title="GCD_1:NM.3">gcdDomain</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">Amp</font> being   <a href="gcd_1.html#M2" title="GCD_1:mode.2">AmpleSet</a> of <font color="Maroon" title="c1">R</font><br/> for <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font>, <font color="Olive" title="b4">c</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font> holds   <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">a</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">b</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Olive" title="b4">c</font></span>)</span></span>)</span>,<font color="Olive" title="b4">c</font>,<font color="Olive" title="b1">Amp</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Olive" title="b2">a</font>,<font color="Olive" title="b4">c</font>,<font color="Olive" title="b1">Amp</font></span><br/><b>let </b><font color="Maroon" title="c2">Amp</font> be    <a href="gcd_1.html#M2" title="GCD_1:mode.2">AmpleSet</a> of <font color="Maroon" title="c1">R</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font> holds   <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">b</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Olive" title="b3">c</font></span>)</span></span>)</span>,<font color="Olive" title="b3">c</font>,<font color="Maroon" title="c2">Amp</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font>,<font color="Maroon" title="c2">Amp</font></span><br/><b>let </b><font color="Maroon" title="c3">A</font>, <font color="Maroon" title="c4">B</font>, <font color="Maroon" title="c5">C</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">C</font></span>)</span></span>)</span>,<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c2">Amp</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c2">Amp</font></span><br/>





<b>set </b><font color="Maroon" title="c6">D</font> =  <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c2">Amp</font>;<br/>
<a NAME="E1:66"/><i><font color="Green" title="E49">A1</font></i>: 
(  <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c2">Amp</font> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <font color="Maroon" title="c3">A</font> &amp;  <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c2">Amp</font> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <font color="Maroon" title="c5">C</font> )
 
<b>by </b><i><a class="ref" href="gcd_1.html#D12" target="_self" title="GCD_1:def.12">Def12</a></i>;<br/>
<a NAME="E2:66"/><i><font color="Green" title="E50">A2</font></i>: 
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c2">Amp</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">Amp</font>
 
<b>by </b><i><a class="ref" href="gcd_1.html#D12" target="_self" title="GCD_1:def.12">Def12</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c7">E</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font><b> such that </b><br/><a NAME="E4:66"/><i><font color="Green" title="E51">A3</font></i>: 
<span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c7">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">A</font>
 <b>by </b><i><a class="txt" href="gcd_1.html#E1:66"><i><font color="Green" title="E49">A1</font></i></a>, <a class="ref" href="gcd_1.html#D1" target="_self" title="GCD_1:def.1">Def1</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c8">F</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font><b> such that </b><br/><a NAME="E6:66"/><i><font color="Green" title="E52">A4</font></i>: 
<span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c8">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">C</font>
 <b>by </b><i><a class="txt" href="gcd_1.html#E1:66"><i><font color="Green" title="E49">A1</font></i></a>, <a class="ref" href="gcd_1.html#D1" target="_self" title="GCD_1:def.1">Def1</a></i>;<br/>
<a NAME="E7:66"/><i><font color="Green" title="E53">A5</font></i>: 
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c2">Amp</font> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <font color="Maroon" title="c3">A</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">C</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="66_1"><b>proof </b></a><div class="add">

<span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">E</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">F</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c4">B</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c7">E</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">F</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c4">B</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#D11" title="VECTSP_1:def.11">VECTSP_1:def 11</a></i>
<br/>.= 
<font color="Maroon" title="c3">A</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">C</font></span>)</span>
<b>by </b><i><a class="txt" href="gcd_1.html#E4:66"><i><font color="Green" title="E51">A3</font></i></a>, <a class="txt" href="gcd_1.html#E6:66"><i><font color="Green" title="E52">A4</font></i></a>, <a class="ref" href="group_1.html#D4" title="GROUP_1:def.4">GROUP_1:def 4</a></i>
;<br/>
<b>hence </b><a NAME="E2:66_1"/>
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c2">Amp</font> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <font color="Maroon" title="c3">A</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">C</font></span>)</span>
 <b>by </b><i><a class="ref" href="gcd_1.html#D1" target="_self" title="GCD_1:def.1">Def1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E8:66"/>
for <font color="Olive" title="b1">z</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font>  st <font color="Olive" title="b1">z</font> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <font color="Maroon" title="c3">A</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">C</font></span>)</span> &amp; <font color="Olive" title="b1">z</font> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <font color="Maroon" title="c5">C</font> holds <br/><font color="Olive" title="b1">z</font> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a>  <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c2">Amp</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="66_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c9">Z</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c9">Z</font> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <font color="Maroon" title="c3">A</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">C</font></span>)</span> &amp; <font color="Maroon" title="c9">Z</font> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <font color="Maroon" title="c5">C</font> implies <font color="Maroon" title="c9">Z</font> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a>  <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c2">Amp</font> )</span><br/>

<b>assume </b><a NAME="E1:66_2"/><i><font color="Green" title="E54">A6</font></i>: 
( <font color="Maroon" title="c9">Z</font> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <font color="Maroon" title="c3">A</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">C</font></span>)</span> &amp; <font color="Maroon" title="c9">Z</font> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <font color="Maroon" title="c5">C</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c9">Z</font> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a>  <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c2">Amp</font></span><br/>

<b>then consider </b><font color="Maroon" title="c10">X</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font><b> such that </b><br/><a NAME="E3:66_2"/><i><font color="Green" title="E55">A7</font></i>: 
<font color="Maroon" title="c9">Z</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c10">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">C</font>
 <b>by </b><i><a class="ref" href="gcd_1.html#D1" target="_self" title="GCD_1:def.1">Def1</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c11">Y</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font><b> such that </b><br/><a NAME="E5:66_2"/><i><font color="Green" title="E56">A8</font></i>: 
<font color="Maroon" title="c9">Z</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c11">Y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">A</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">C</font></span>)</span>
 <b>by </b><i><a class="txt" href="gcd_1.html#E1:66_2"><i><font color="Green" title="E54">A6</font></i></a>, <a class="ref" href="gcd_1.html#D1" target="_self" title="GCD_1:def.1">Def1</a></i>;<br/>
<font color="Maroon" title="c9">Z</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">Y</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c10">X</font></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">Z</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c11">Y</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="c9">Z</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c10">X</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#D11" title="VECTSP_1:def.11">VECTSP_1:def 11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">Z</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c11">Y</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">Z</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">X</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c4">B</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#T40" title="VECTSP_1:th.40">VECTSP_1:40</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">C</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c4">B</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="gcd_1.html#E3:66_2"><i><font color="Green" title="E55">A7</font></i></a>, <a class="txt" href="gcd_1.html#E5:66_2"><i><font color="Green" title="E56">A8</font></i></a>, <a class="ref" href="group_1.html#D4" title="GROUP_1:def.4">GROUP_1:def 4</a></i>
<br/>.= 
<font color="Maroon" title="c3">A</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">C</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c4">B</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D6" title="RLVECT_1:def.6">RLVECT_1:def 6</a></i>
<br/>.= 
<font color="Maroon" title="c3">A</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D11" title="RLVECT_1:def.11">RLVECT_1:def 11</a></i>
<br/>.= 
<font color="Maroon" title="c3">A</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T10" title="RLVECT_1:th.10">RLVECT_1:10</a></i>
;<br/>
<a NAME="E7:66_2"/><b>then </b>
<font color="Maroon" title="c9">Z</font> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <font color="Maroon" title="c3">A</font>
 
<b>by </b><i><a class="ref" href="gcd_1.html#D1" target="_self" title="GCD_1:def.1">Def1</a></i>;<br/>
<b>hence </b><a NAME="E8:66_2"/>
<font color="Maroon" title="c9">Z</font> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a>  <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c2">Amp</font>
 <b>by </b><i><a class="txt" href="gcd_1.html#E1:66_2"><i><font color="Green" title="E54">A6</font></i></a>, <a class="ref" href="gcd_1.html#D12" target="_self" title="GCD_1:def.12">Def12</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E9:66"/>
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">C</font></span>)</span></span>)</span>,<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c2">Amp</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c2">Amp</font>
 <b>by </b><i><a class="txt" href="gcd_1.html#E1:66"><i><font color="Green" title="E49">A1</font></i></a>, <a class="txt" href="gcd_1.html#E2:66"><i><font color="Green" title="E50">A2</font></i></a>, <a class="txt" href="gcd_1.html#E7:66"><i><font color="Green" title="E53">A5</font></i></a>, <a class="ref" href="gcd_1.html#D12" target="_self" title="GCD_1:def.12">Def12</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
