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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">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>  st <font color="Olive" title="b3">b</font> <a href="gcd_1.html#R4" title="GCD_1:pred.4">is_associated_to</a> <font color="Olive" title="b4">c</font> holds <br/>(  <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> <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="Olive" title="b2">a</font>,<font color="Olive" title="b4">c</font>,<font color="Olive" title="b1">Amp</font> &amp;  <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Olive" title="b3">b</font>,<font color="Olive" title="b2">a</font>,<font color="Olive" title="b1">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="Olive" title="b4">c</font>,<font color="Olive" title="b2">a</font>,<font color="Olive" title="b1">Amp</font> )</span><br/><b>let </b><font color="Maroon" title="c2">Amp</font> be    <a href="gcd_1.html#M2" title="GCD_1:mode.2">AmpleSet</a> of <font color="Maroon" title="c1">R</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font>  st <font color="Olive" title="b2">b</font> <a href="gcd_1.html#R4" title="GCD_1:pred.4">is_associated_to</a> <font color="Olive" title="b3">c</font> holds <br/>(  <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> <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="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font>,<font color="Maroon" title="c2">Amp</font> &amp;  <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b1">a</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="Olive" title="b3">c</font>,<font color="Olive" title="b1">a</font>,<font color="Maroon" title="c2">Amp</font> )</span><br/><b>let </b><font color="Maroon" title="c3">A</font>, <font color="Maroon" title="c4">B</font>, <font color="Maroon" title="c5">C</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">B</font> <a href="gcd_1.html#R4" title="GCD_1:pred.4">is_associated_to</a> <font color="Maroon" title="c5">C</font> implies (  <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> <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>,<font color="Maroon" title="c5">C</font>,<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="c4">B</font>,<font color="Maroon" title="c3">A</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="c5">C</font>,<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c2">Amp</font> ) )</span><br/>





<b>assume </b><a NAME="E1:61"/><i><font color="Green" title="E44">A1</font></i>: 
<font color="Maroon" title="c4">B</font> <a href="gcd_1.html#R4" title="GCD_1:pred.4">is_associated_to</a> <font color="Maroon" title="c5">C</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <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> <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>,<font color="Maroon" title="c5">C</font>,<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="c4">B</font>,<font color="Maroon" title="c3">A</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="c5">C</font>,<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c2">Amp</font> )</span><br/>

<a NAME="E2:61"/><b>then </b><i><font color="Green" title="E45">A2</font></i>: 
<font color="Maroon" title="c4">B</font> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <font color="Maroon" title="c5">C</font>
 
<b>by </b><i><a class="ref" href="gcd_1.html#D3" target="_self" title="GCD_1:def.3">Def3</a></i>;<br/>
<a NAME="E3:61"/>
 <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> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <font color="Maroon" title="c4">B</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="E4:61"/><b>then </b><i><font color="Green" title="E46">A3</font></i>: 
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c2">Amp</font> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <font color="Maroon" title="c5">C</font>
 
<b>by </b><i><a class="txt" href="gcd_1.html#E2:61"><i><font color="Green" title="E45">A2</font></i></a>, <a class="ref" href="gcd_1.html#T2" target="_self" title="GCD_1:th.2">Th2</a></i>;<br/>
<a NAME="E5:61"/>
 <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> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <font color="Maroon" title="c3">A</font>
 
<b>by </b><i><a class="ref" href="gcd_1.html#D12" target="_self" title="GCD_1:def.12">Def12</a></i>;<br/>
<a NAME="E6:61"/><b>then </b><i><font color="Green" title="E47">A4</font></i>: 
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c4">B</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="c5">C</font>,<font color="Maroon" title="c2">Amp</font>
 
<b>by </b><i><a class="txt" href="gcd_1.html#E4:61"><i><font color="Green" title="E46">A3</font></i></a>, <a class="ref" href="gcd_1.html#D12" target="_self" title="GCD_1:def.12">Def12</a></i>;<br/>
<a NAME="E7:61"/><i><font color="Green" title="E48">A5</font></i>: 
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c4">B</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="c4">B</font>,<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c2">Amp</font>
 
<b>by </b><i><a class="ref" href="gcd_1.html#T30" target="_self" title="GCD_1:th.30">Th30</a></i>;<br/>
<a NAME="E8:61"/><i><font color="Green" title="E49">A6</font></i>: 
<font color="Maroon" title="c5">C</font> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <font color="Maroon" title="c4">B</font>
 
<b>by </b><i><a class="txt" href="gcd_1.html#E1:61"><i><font color="Green" title="E44">A1</font></i></a>, <a class="ref" href="gcd_1.html#D3" target="_self" title="GCD_1:def.3">Def3</a></i>;<br/>
<a NAME="E9:61"/>
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c2">Amp</font> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <font color="Maroon" title="c5">C</font>
 
<b>by </b><i><a class="ref" href="gcd_1.html#D12" target="_self" title="GCD_1:def.12">Def12</a></i>;<br/>
<a NAME="E10:61"/><b>then </b><i><font color="Green" title="E50">A7</font></i>: 
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c2">Amp</font> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <font color="Maroon" title="c4">B</font>
 
<b>by </b><i><a class="txt" href="gcd_1.html#E8:61"><i><font color="Green" title="E49">A6</font></i></a>, <a class="ref" href="gcd_1.html#T2" target="_self" title="GCD_1:th.2">Th2</a></i>;<br/>
<a NAME="E11:61"/>
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c2">Amp</font> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <font color="Maroon" title="c3">A</font>
 
<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="E12:61"/><b>then </b>
 <a href="gcd_1.html#K5" title="GCD_1:func.5">gcd</a> <font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c2">Amp</font> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a>  <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>
 
<b>by </b><i><a class="txt" href="gcd_1.html#E10:61"><i><font color="Green" title="E50">A7</font></i></a>, <a class="ref" href="gcd_1.html#D12" target="_self" title="GCD_1:def.12">Def12</a></i>;<br/>
<a NAME="E13:61"/><b>then </b>
 <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> <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>,<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c2">Amp</font>
 
<b>by </b><i><a class="txt" href="gcd_1.html#E6:61"><i><font color="Green" title="E47">A4</font></i></a>, <a class="ref" href="gcd_1.html#D3" target="_self" title="GCD_1:def.3">Def3</a></i>;<br/>
<b>hence </b><a NAME="E14:61"/>
(  <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> <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>,<font color="Maroon" title="c5">C</font>,<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="c4">B</font>,<font color="Maroon" title="c3">A</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="c5">C</font>,<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c2">Amp</font> )
 <b>by </b><i><a class="txt" href="gcd_1.html#E7:61"><i><font color="Green" title="E48">A5</font></i></a>, <a class="ref" href="gcd_1.html#T30" target="_self" title="GCD_1:th.30">Th30</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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