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<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">r1</font>, <font color="Olive" title="b3">r2</font>, <font color="Olive" title="b4">s1</font>, <font color="Olive" title="b5">s2</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font>  st  <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Olive" title="b2">r1</font>,<font color="Olive" title="b3">r2</font>,<font color="Olive" title="b1">Amp</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">R</font> &amp;  <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Olive" title="b4">s1</font>,<font color="Olive" title="b5">s2</font>,<font color="Olive" title="b1">Amp</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">R</font> &amp; <font color="Olive" title="b3">r2</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> <font color="Maroon" title="c1">R</font> &amp; <font color="Olive" title="b5">s2</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> <font color="Maroon" title="c1">R</font> holds <br/> <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">r1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p3">(<span class="default"><font color="Olive" title="b5">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p4">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Olive" title="b3">r2</font>,<font color="Olive" title="b5">s2</font>,<font color="Olive" title="b1">Amp</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Olive" title="b4">s1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p3">(<span class="default"><font color="Olive" title="b3">r2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p4">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Olive" title="b3">r2</font>,<font color="Olive" title="b5">s2</font>,<font color="Olive" title="b1">Amp</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b3">r2</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Olive" title="b5">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p3">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Olive" title="b3">r2</font>,<font color="Olive" title="b5">s2</font>,<font color="Olive" title="b1">Amp</font></span>)</span></span>)</span></span>)</span>,<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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">r1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p3">(<span class="default"><font color="Olive" title="b5">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p4">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Olive" title="b3">r2</font>,<font color="Olive" title="b5">s2</font>,<font color="Olive" title="b1">Amp</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Olive" title="b4">s1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p3">(<span class="default"><font color="Olive" title="b3">r2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p4">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Olive" title="b3">r2</font>,<font color="Olive" title="b5">s2</font>,<font color="Olive" title="b1">Amp</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Olive" title="b3">r2</font>,<font color="Olive" title="b5">s2</font>,<font color="Olive" title="b1">Amp</font></span>)</span>,<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">r1</font>, <font color="Olive" title="b2">r2</font>, <font color="Olive" title="b3">s1</font>, <font color="Olive" title="b4">s2</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font>  st  <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Olive" title="b1">r1</font>,<font color="Olive" title="b2">r2</font>,<font color="Maroon" title="c2">Amp</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">R</font> &amp;  <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Olive" title="b3">s1</font>,<font color="Olive" title="b4">s2</font>,<font color="Maroon" title="c2">Amp</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">R</font> &amp; <font color="Olive" title="b2">r2</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> <font color="Maroon" title="c1">R</font> &amp; <font color="Olive" title="b4">s2</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> <font color="Maroon" title="c1">R</font> holds <br/> <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">r1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p3">(<span class="default"><font color="Olive" title="b4">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p4">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Olive" title="b2">r2</font>,<font color="Olive" title="b4">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">s1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p3">(<span class="default"><font color="Olive" title="b2">r2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p4">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Olive" title="b2">r2</font>,<font color="Olive" title="b4">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b2">r2</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Olive" title="b4">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p3">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Olive" title="b2">r2</font>,<font color="Olive" title="b4">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span></span>)</span>,<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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">r1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p3">(<span class="default"><font color="Olive" title="b4">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p4">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Olive" title="b2">r2</font>,<font color="Olive" title="b4">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">s1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p3">(<span class="default"><font color="Olive" title="b2">r2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p4">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Olive" title="b2">r2</font>,<font color="Olive" title="b4">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Olive" title="b2">r2</font>,<font color="Olive" title="b4">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span>,<font color="Maroon" title="c2">Amp</font></span><br/><b>let </b><font color="Maroon" title="c3">r1</font>, <font color="Maroon" title="c4">r2</font>, <font color="Maroon" title="c5">s1</font>, <font color="Maroon" title="c6">s2</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> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c2">Amp</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">R</font> &amp;  <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">R</font> &amp; <font color="Maroon" title="c4">r2</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> <font color="Maroon" title="c1">R</font> &amp; <font color="Maroon" title="c6">s2</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> <font color="Maroon" title="c1">R</font> implies  <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p4">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">s1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p4">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p3">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span></span>)</span>,<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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p4">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">s1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p4">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span>,<font color="Maroon" title="c2">Amp</font> )</span><br/>





<b>assume </b><a NAME="E1:67"/><i><font color="Green" title="E50">A1</font></i>: 
(  <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c2">Amp</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">R</font> &amp;  <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">R</font> &amp; <font color="Maroon" title="c4">r2</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> <font color="Maroon" title="c1">R</font> &amp; <font color="Maroon" title="c6">s2</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> <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"><span class="p2">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p4">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">s1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p4">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p3">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span></span>)</span>,<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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p4">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">s1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p4">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span>,<font color="Maroon" title="c2">Amp</font></span><br/>

<b>set </b><font color="Maroon" title="c7">d</font> =  <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font>;<br/>
<a NAME="E2:67"/><i><font color="Green" title="E51">A2</font></i>: 
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</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="c6">s2</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="E3:67"/><i><font color="Green" title="E52">A3</font></i>: 
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</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="c4">r2</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="E4:67"/><i><font color="Green" title="E53">A4</font></i>: 
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</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> <font color="Maroon" title="c1">R</font>
 
<b>by </b><i><a class="txt" href="#E1:67"><i><font color="Green" title="E50">A1</font></i></a>, <a class="ref" href="gcd_1.html#T34" target="_self" title="GCD_1:th.34">Th34</a></i>;<br/>
<b>set </b><font color="Maroon" title="c8">r</font> = <font color="Maroon" title="c4">r2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c9">s</font> = <font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span>;<br/>
<a NAME="E5:67"/><i><font color="Green" title="E54">A5</font></i>: 
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p4">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">s1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p4">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span>,<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> <span class="p1">(<span class="default"><font color="Maroon" title="c5">s1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p3">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">Amp</font>
 
<b>by </b><i><a class="ref" href="gcd_1.html#T40" target="_self" title="GCD_1:th.40">Th40</a></i>;<br/>
<a NAME="E6:67"/>
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span>,<font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c2">Amp</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">R</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_1"><b>proof </b></a><div class="add">

<a NAME="E1:67_1"/><i><font color="Green" title="E55">A6</font></i>: 
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span>,<font color="Maroon" title="c5">s1</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">s1</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="E2:67_1"/>
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span>,<font color="Maroon" title="c5">s1</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="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span>
 
<b>by </b><i><a class="ref" href="gcd_1.html#D12" target="_self" title="GCD_1:def.12">Def12</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c10">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="E4:67_1"/><i><font color="Green" title="E56">A7</font></i>: 
<span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p3">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span>,<font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c10">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</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>;<br/>
<span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p3">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span>,<font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">e</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span>
<b>by </b><i><a class="txt" href="#E4:67_1"><i><font color="Green" title="E56">A7</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="c6">s2</font>
<b>by </b><i><a class="txt" href="#E2:67"><i><font color="Green" title="E51">A2</font></i></a>, <a class="txt" href="#E4:67"><i><font color="Green" title="E53">A4</font></i></a>, <a class="ref" href="gcd_1.html#D4" target="_self" title="GCD_1:def.4">Def4</a></i>
;<br/>
<a NAME="E6:67_1"/><b>then </b>
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span>,<font color="Maroon" title="c5">s1</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="c6">s2</font>
 
<b>by </b><i><a class="ref" href="gcd_1.html#D1" target="_self" title="GCD_1:def.1">Def1</a></i>;<br/>
<a NAME="E7:67_1"/><b>then </b><i><font color="Green" title="E57">A8</font></i>: 
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span>,<font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c2">Amp</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="c5">s1</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font>
 
<b>by </b><i><a class="txt" href="#E1:67_1"><i><font color="Green" title="E55">A6</font></i></a>, <a class="ref" href="gcd_1.html#D12" target="_self" title="GCD_1:def.12">Def12</a></i>;<br/>
<a NAME="E8:67_1"/>
<span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p3">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span>,<font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span>,<font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c2">Amp</font>
 
<b>by </b><i><a class="ref" href="vectsp_1.html#D19" title="VECTSP_1:def.19">VECTSP_1:def 19</a></i>;<br/>
<a NAME="E9:67_1"/><b>then </b>
 <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">R</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> <span class="p1">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span>,<font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c2">Amp</font>
 
<b>by </b><i><a class="ref" href="gcd_1.html#D1" target="_self" title="GCD_1:def.1">Def1</a></i>;<br/>
<a NAME="E10:67_1"/><b>then </b><i><font color="Green" title="E58">A9</font></i>: 
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span>,<font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c2">Amp</font> <a href="gcd_1.html#R4" title="GCD_1:pred.4">is_associated_to</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">R</font>
 
<b>by </b><i><a class="txt" href="#E1:67"><i><font color="Green" title="E50">A1</font></i></a>, <a class="txt" href="#E7:67_1"><i><font color="Green" title="E57">A8</font></i></a>, <a class="ref" href="gcd_1.html#D3" target="_self" title="GCD_1:def.3">Def3</a></i>;<br/>
<a NAME="E11:67_1"/><i><font color="Green" title="E59">A10</font></i>: 
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span>,<font color="Maroon" title="c5">s1</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/>
<a NAME="E12:67_1"/>
 <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">R</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#D8" target="_self" title="GCD_1:def.8">Def8</a></i>;<br/>
<b>hence </b><a NAME="E13:67_1"/>
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span>,<font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c2">Amp</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">R</font>
 <b>by </b><i><a class="txt" href="#E10:67_1"><i><font color="Green" title="E58">A9</font></i></a>, <a class="txt" href="#E11:67_1"><i><font color="Green" title="E59">A10</font></i></a>, <a class="ref" href="gcd_1.html#T22" target="_self" title="GCD_1:th.22">Th22</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="E7:67"/><b>then </b><i><font color="Green" title="E55">A11</font></i>: 
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">s1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p3">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span></span>)</span>,<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> <span class="p1">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">Amp</font>
 
<b>by </b><i><a class="ref" href="gcd_1.html#T38" target="_self" title="GCD_1:th.38">Th38</a></i>;<br/>
<a NAME="E8:67"/><i><font color="Green" title="E56">A12</font></i>: 
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">Amp</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">R</font>
 
<b>by </b><i><a class="txt" href="#E4:67"><i><font color="Green" title="E53">A4</font></i></a>, <a class="ref" href="gcd_1.html#T39" target="_self" title="GCD_1:th.39">Th39</a></i>;<br/>
<i><font color="Green" title="E57">A13</font></i>:  <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p4">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">s1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p4">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">Amp</font> = 
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">s1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p3">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c2">Amp</font>
<b>by </b><i><a class="txt" href="#E5:67"><i><font color="Green" title="E54">A5</font></i></a>, <a class="ref" href="gcd_1.html#T30" target="_self" title="GCD_1:th.30">Th30</a></i>
<br/>.= 
 <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">R</font>
<b>by </b><i><a class="txt" href="#E7:67"><i><font color="Green" title="E55">A11</font></i></a>, <a class="txt" href="#E8:67"><i><font color="Green" title="E56">A12</font></i></a>, <a class="ref" href="gcd_1.html#T30" target="_self" title="GCD_1:th.30">Th30</a></i>
;<br/>
<a NAME="E10:67"/><i><font color="Green" title="E58">A14</font></i>: 
<font color="Maroon" title="c4">r2</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</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="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p3">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_3"><b>proof </b></a><div class="add">

<a NAME="E1:67_3"/><i><font color="Green" title="E59">A15</font></i>: 
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c4">r2</font>
 
<b>by </b><i><a class="ref" href="gcd_1.html#T6" target="_self" title="GCD_1:th.6">Th6</a></i>;<br/>
<font color="Maroon" title="c4">r2</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c4">r2</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#D19" title="VECTSP_1:def.19">VECTSP_1:def 19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p3">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c4">r2</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E4:67"><i><font color="Green" title="E53">A4</font></i></a>, <a class="ref" href="gcd_1.html#T9" target="_self" title="GCD_1:th.9">Th9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c4">r2</font></span>)</span> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E4:67"><i><font color="Green" title="E53">A4</font></i></a>, <a class="txt" href="#E1:67_3"><i><font color="Green" title="E59">A15</font></i></a>, <a class="ref" href="gcd_1.html#T11" target="_self" title="GCD_1:th.11">Th11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</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="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p3">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E3:67"><i><font color="Green" title="E52">A3</font></i></a>, <a class="txt" href="#E4:67"><i><font color="Green" title="E53">A4</font></i></a>, <a class="txt" href="#E1:67_3"><i><font color="Green" title="E59">A15</font></i></a>, <a class="ref" href="gcd_1.html#T11" target="_self" title="GCD_1:th.11">Th11</a></i>
;<br/>
<b>hence </b><a NAME="E3:67_3"/>
<font color="Maroon" title="c4">r2</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</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="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p3">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span></span>)</span>
 ; <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="E11:67"/><i><font color="Green" title="E59">A16</font></i>: 
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p4">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">s1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p4">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span>,<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> <span class="p1">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p3">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">Amp</font>
 
<b>by </b><i><a class="ref" href="gcd_1.html#T40" target="_self" title="GCD_1:th.40">Th40</a></i>;<br/>
<a NAME="E12:67"/>
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c2">Amp</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">R</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_4"><b>proof </b></a><div class="add">

<a NAME="E1:67_4"/><i><font color="Green" title="E60">A17</font></i>: 
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">r1</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">r1</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="E2:67_4"/>
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">r1</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="c4">r2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span>
 
<b>by </b><i><a class="ref" href="gcd_1.html#D12" target="_self" title="GCD_1:def.12">Def12</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c10">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="E4:67_4"/><i><font color="Green" title="E61">A18</font></i>: 
<span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p3">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c10">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">r2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</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>;<br/>
<span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p3">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">e</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span>
<b>by </b><i><a class="txt" href="#E4:67_4"><i><font color="Green" title="E61">A18</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="c4">r2</font>
<b>by </b><i><a class="txt" href="#E3:67"><i><font color="Green" title="E52">A3</font></i></a>, <a class="txt" href="#E4:67"><i><font color="Green" title="E53">A4</font></i></a>, <a class="ref" href="gcd_1.html#D4" target="_self" title="GCD_1:def.4">Def4</a></i>
;<br/>
<a NAME="E6:67_4"/><b>then </b>
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">r1</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="c4">r2</font>
 
<b>by </b><i><a class="ref" href="gcd_1.html#D1" target="_self" title="GCD_1:def.1">Def1</a></i>;<br/>
<a NAME="E7:67_4"/><b>then </b><i><font color="Green" title="E62">A19</font></i>: 
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c2">Amp</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">r1</font>,<font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c2">Amp</font>
 
<b>by </b><i><a class="txt" href="#E1:67_4"><i><font color="Green" title="E60">A17</font></i></a>, <a class="ref" href="gcd_1.html#D12" target="_self" title="GCD_1:def.12">Def12</a></i>;<br/>
<a NAME="E8:67_4"/>
<span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p3">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c2">Amp</font>
 
<b>by </b><i><a class="ref" href="vectsp_1.html#D19" title="VECTSP_1:def.19">VECTSP_1:def 19</a></i>;<br/>
<a NAME="E9:67_4"/><b>then </b>
 <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">R</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> <span class="p1">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c2">Amp</font>
 
<b>by </b><i><a class="ref" href="gcd_1.html#D1" target="_self" title="GCD_1:def.1">Def1</a></i>;<br/>
<a NAME="E10:67_4"/><b>then </b><i><font color="Green" title="E63">A20</font></i>: 
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c2">Amp</font> <a href="gcd_1.html#R4" title="GCD_1:pred.4">is_associated_to</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">R</font>
 
<b>by </b><i><a class="txt" href="#E1:67"><i><font color="Green" title="E50">A1</font></i></a>, <a class="txt" href="#E7:67_4"><i><font color="Green" title="E62">A19</font></i></a>, <a class="ref" href="gcd_1.html#D3" target="_self" title="GCD_1:def.3">Def3</a></i>;<br/>
<a NAME="E11:67_4"/><i><font color="Green" title="E64">A21</font></i>: 
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">r1</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/>
<a NAME="E12:67_4"/>
 <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">R</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#D8" target="_self" title="GCD_1:def.8">Def8</a></i>;<br/>
<b>hence </b><a NAME="E13:67_4"/>
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">r1</font>,<font color="Maroon" title="c2">Amp</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">R</font>
 <b>by </b><i><a class="txt" href="#E10:67_4"><i><font color="Green" title="E63">A20</font></i></a>, <a class="txt" href="#E11:67_4"><i><font color="Green" title="E64">A21</font></i></a>, <a class="ref" href="gcd_1.html#T22" target="_self" title="GCD_1:th.22">Th22</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="E13:67"/><b>then </b><i><font color="Green" title="E60">A22</font></i>: 
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p3">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span></span>)</span>,<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> <span class="p1">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">Amp</font>
 
<b>by </b><i><a class="ref" href="gcd_1.html#T38" target="_self" title="GCD_1:th.38">Th38</a></i>;<br/>
<a NAME="E14:67"/>
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p2">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">Amp</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">R</font>
 
<b>by </b><i><a class="txt" href="#E4:67"><i><font color="Green" title="E53">A4</font></i></a>, <a class="ref" href="gcd_1.html#T39" target="_self" title="GCD_1:th.39">Th39</a></i>;<br/>
<a NAME="E15:67"/><b>then </b>
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p4">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">s1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p4">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span></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="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p3">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span></span>)</span>,<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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p4">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">s1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p4">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span>,<font color="Maroon" title="c2">Amp</font>
 
<b>by </b><i><a class="txt" href="#E11:67"><i><font color="Green" title="E59">A16</font></i></a>, <a class="txt" href="#E13:67"><i><font color="Green" title="E60">A22</font></i></a>, <a class="ref" href="gcd_1.html#T30" target="_self" title="GCD_1:th.30">Th30</a>, <a class="ref" href="gcd_1.html#T38" target="_self" title="GCD_1:th.38">Th38</a></i>;<br/>
<b>hence </b><a NAME="E16:67"/>
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p4">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">s1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p4">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p3">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span></span>)</span>,<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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">r1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">s2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p4">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">s1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">r2</font> <a href="gcd_1.html#K1" title="GCD_1:func.1">/</a> <span class="p4">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c4">r2</font>,<font color="Maroon" title="c6">s2</font>,<font color="Maroon" title="c2">Amp</font></span>)</span>,<font color="Maroon" title="c2">Amp</font>
 <b>by </b><i><a class="txt" href="#E9:67"><i><font color="Green" title="E57">A13</font></i></a>, <a class="txt" href="#E10:67"><i><font color="Green" title="E58">A14</font></i></a>, <a class="ref" href="gcd_1.html#T38" target="_self" title="GCD_1:th.38">Th38</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>
