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<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> (<font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font>,<font color="Olive" title="b1">Amp</font>)</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>,<span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> (<font color="Olive" title="b3">b</font>,<font color="Olive" title="b4">c</font>,<font color="Olive" title="b1">Amp</font>)</span>)</span>,<font color="Olive" title="b1">Amp</font>)</span><br/><span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Maroon" title="c2">Amp</font>)</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>,<span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> (<font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font>,<font color="Maroon" title="c2">Amp</font>)</span>)</span>,<font color="Maroon" title="c2">Amp</font>)</span><br/><span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> (<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="c4">B</font>,<font color="Maroon" title="c2">Amp</font>)</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>,<span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> (<font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c2">Amp</font>)</span>)</span>,<font color="Maroon" title="c2">Amp</font>)</span><br/>





<span class="kw">set </span><font color="Maroon" title="c6">D</font> =  <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> (<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="c4">B</font>,<font color="Maroon" title="c2">Amp</font>)</span>)</span>,<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c2">Amp</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c7">E</font> =  <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> (<font color="Maroon" title="c3">A</font>,<span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> (<font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c2">Amp</font>)</span>)</span>,<font color="Maroon" title="c2">Amp</font>);<br/>
<a NAME="E1:62"/><span class="lab"><font color="Green" title="E45">A1</font></span>: 
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> (<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="c4">B</font>,<font color="Maroon" title="c2">Amp</font>)</span>)</span>,<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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="gcd_1.html#D12" target="_self" title="GCD_1:def.12">Def12</a></span>;<br/>
<a NAME="E2:62"/><span class="lab"><font color="Green" title="E46">A2</font></span>: 
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> (<font color="Maroon" title="c3">A</font>,<span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> (<font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c2">Amp</font>)</span>)</span>,<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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="gcd_1.html#D12" target="_self" title="GCD_1:def.12">Def12</a></span>;<br/>
<a NAME="E3:62"/><span class="lab"><font color="Green" title="E47">A3</font></span>: 
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> (<font color="Maroon" title="c3">A</font>,<span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> (<font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c2">Amp</font>)</span>)</span>,<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="c4">B</font>,<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c2">Amp</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="gcd_1.html#D12" target="_self" title="GCD_1:def.12">Def12</a></span>;<br/>
<a NAME="E4:62"/><span class="kw">then </span><span class="lab"><font color="Green" title="E48">A4</font></span>: 
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> (<font color="Maroon" title="c3">A</font>,<span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> (<font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c2">Amp</font>)</span>)</span>,<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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="gcd_1.html#T28" target="_self" title="GCD_1:th.28">Th29</a></span>;<br/>
<a NAME="E5:62"/>
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> (<font color="Maroon" title="c3">A</font>,<span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> (<font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c2">Amp</font>)</span>)</span>,<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">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:62"><span class="lab"><font color="Green" title="E47">A3</font></span></a>, <a class="ref" href="gcd_1.html#T28" target="_self" title="GCD_1:th.28">Th29</a></span>;<br/>
<a NAME="E6:62"/><span class="kw">then </span>
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> (<font color="Maroon" title="c3">A</font>,<span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> (<font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c2">Amp</font>)</span>)</span>,<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">A</font>,<font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c2">Amp</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:62"><span class="lab"><font color="Green" title="E46">A2</font></span></a>, <a class="ref" href="gcd_1.html#D12" target="_self" title="GCD_1:def.12">Def12</a></span>;<br/>
<a NAME="E7:62"/><span class="kw">then </span><span class="lab"><font color="Green" title="E49">A5</font></span>: 
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> (<font color="Maroon" title="c3">A</font>,<span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> (<font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c2">Amp</font>)</span>)</span>,<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> (<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="c4">B</font>,<font color="Maroon" title="c2">Amp</font>)</span>)</span>,<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c2">Amp</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:62"><span class="lab"><font color="Green" title="E48">A4</font></span></a>, <a class="ref" href="gcd_1.html#D12" target="_self" title="GCD_1:def.12">Def12</a></span>;<br/>
<a NAME="E8:62"/><span class="lab"><font color="Green" title="E50">A6</font></span>: 
(  <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> (<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="c4">B</font>,<font color="Maroon" title="c2">Amp</font>)</span>)</span>,<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> &amp;  <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> (<font color="Maroon" title="c3">A</font>,<span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> (<font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c2">Amp</font>)</span>)</span>,<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> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="gcd_1.html#D12" target="_self" title="GCD_1:def.12">Def12</a></span>;<br/>
<a NAME="E9:62"/><span class="lab"><font color="Green" title="E51">A7</font></span>: 
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> (<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="c4">B</font>,<font color="Maroon" title="c2">Amp</font>)</span>)</span>,<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>  <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> (<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c2">Amp</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="gcd_1.html#D12" target="_self" title="GCD_1:def.12">Def12</a></span>;<br/>
<a NAME="E10:62"/><span class="kw">then </span><span class="lab"><font color="Green" title="E52">A8</font></span>: 
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> (<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="c4">B</font>,<font color="Maroon" title="c2">Amp</font>)</span>)</span>,<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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="gcd_1.html#T28" target="_self" title="GCD_1:th.28">Th29</a></span>;<br/>
<a NAME="E11:62"/>
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> (<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="c4">B</font>,<font color="Maroon" title="c2">Amp</font>)</span>)</span>,<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="c4">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:62"><span class="lab"><font color="Green" title="E51">A7</font></span></a>, <a class="ref" href="gcd_1.html#T28" target="_self" title="GCD_1:th.28">Th29</a></span>;<br/>
<a NAME="E12:62"/><span class="kw">then </span>
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> (<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="c4">B</font>,<font color="Maroon" title="c2">Amp</font>)</span>)</span>,<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>  <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> (<font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c2">Amp</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:62"><span class="lab"><font color="Green" title="E45">A1</font></span></a>, <a class="ref" href="gcd_1.html#D12" target="_self" title="GCD_1:def.12">Def12</a></span>;<br/>
<a NAME="E13:62"/><span class="kw">then </span>
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> (<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="c4">B</font>,<font color="Maroon" title="c2">Amp</font>)</span>)</span>,<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>  <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> (<font color="Maroon" title="c3">A</font>,<span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> (<font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c2">Amp</font>)</span>)</span>,<font color="Maroon" title="c2">Amp</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:62"><span class="lab"><font color="Green" title="E52">A8</font></span></a>, <a class="ref" href="gcd_1.html#D12" target="_self" title="GCD_1:def.12">Def12</a></span>;<br/>
<a NAME="E14:62"/><span class="kw">then </span>
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> (<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="c4">B</font>,<font color="Maroon" title="c2">Amp</font>)</span>)</span>,<font color="Maroon" title="c5">C</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="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> (<font color="Maroon" title="c3">A</font>,<span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> (<font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c2">Amp</font>)</span>)</span>,<font color="Maroon" title="c2">Amp</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:62"><span class="lab"><font color="Green" title="E49">A5</font></span></a>, <a class="ref" href="gcd_1.html#D3" target="_self" title="GCD_1:def.3">Def3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E15:62"/>
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> (<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="c4">B</font>,<font color="Maroon" title="c2">Amp</font>)</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>,<span class="p1">(<span class="default"><a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> (<font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c2">Amp</font>)</span>)</span>,<font color="Maroon" title="c2">Amp</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:62"><span class="lab"><font color="Green" title="E50">A6</font></span></a>, <a class="ref" href="gcd_1.html#T22" target="_self" title="GCD_1:th.22">Th22</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
