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<b>let </b><font color="Maroon" title="c3">IT1</font>, <font color="Maroon" title="c4">IT2</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">IT1</font> <a href="int_1.html#R2" title="INT_1:pred.2">divides</a> <font color="Maroon" title="c1">a</font> &amp; <font color="Maroon" title="c3">IT1</font> <a href="int_1.html#R2" title="INT_1:pred.2">divides</a> <font color="Maroon" title="c2">b</font> &amp; ( for <font color="Olive" title="b1">m</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>  st <font color="Olive" title="b1">m</font> <a href="int_1.html#R2" title="INT_1:pred.2">divides</a> <font color="Maroon" title="c1">a</font> &amp; <font color="Olive" title="b1">m</font> <a href="int_1.html#R2" title="INT_1:pred.2">divides</a> <font color="Maroon" title="c2">b</font> holds <br/><font color="Olive" title="b1">m</font> <a href="int_1.html#R2" title="INT_1:pred.2">divides</a> <font color="Maroon" title="c3">IT1</font> ) &amp; <font color="Maroon" title="c4">IT2</font> <a href="int_1.html#R2" title="INT_1:pred.2">divides</a> <font color="Maroon" title="c1">a</font> &amp; <font color="Maroon" title="c4">IT2</font> <a href="int_1.html#R2" title="INT_1:pred.2">divides</a> <font color="Maroon" title="c2">b</font> &amp; ( for <font color="Olive" title="b1">m</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>  st <font color="Olive" title="b1">m</font> <a href="int_1.html#R2" title="INT_1:pred.2">divides</a> <font color="Maroon" title="c1">a</font> &amp; <font color="Olive" title="b1">m</font> <a href="int_1.html#R2" title="INT_1:pred.2">divides</a> <font color="Maroon" title="c2">b</font> holds <br/><font color="Olive" title="b1">m</font> <a href="int_1.html#R2" title="INT_1:pred.2">divides</a> <font color="Maroon" title="c4">IT2</font> ) implies <font color="Maroon" title="c3">IT1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">IT2</font> )</span><br/>

<b>assume </b><b>that </b><br/><a NAME="E1:16_1_2"/><i><font color="Green" title="E15">A20</font></i>: 
( <font color="Maroon" title="c3">IT1</font> <a href="int_1.html#R2" title="INT_1:pred.2">divides</a> <font color="Maroon" title="c1">a</font> &amp; <font color="Maroon" title="c3">IT1</font> <a href="int_1.html#R2" title="INT_1:pred.2">divides</a> <font color="Maroon" title="c2">b</font> )
 <b>and </b><br/><a NAME="E2:16_1_2"/><i><font color="Green" title="E16">A21</font></i>: 
for <font color="Olive" title="b1">m</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>  st <font color="Olive" title="b1">m</font> <a href="int_1.html#R2" title="INT_1:pred.2">divides</a> <font color="Maroon" title="c1">a</font> &amp; <font color="Olive" title="b1">m</font> <a href="int_1.html#R2" title="INT_1:pred.2">divides</a> <font color="Maroon" title="c2">b</font> holds <br/><font color="Olive" title="b1">m</font> <a href="int_1.html#R2" title="INT_1:pred.2">divides</a> <font color="Maroon" title="c3">IT1</font>
 <b>and </b><br/><a NAME="E3:16_1_2"/><i><font color="Green" title="E17">A22</font></i>: 
( <font color="Maroon" title="c4">IT2</font> <a href="int_1.html#R2" title="INT_1:pred.2">divides</a> <font color="Maroon" title="c1">a</font> &amp; <font color="Maroon" title="c4">IT2</font> <a href="int_1.html#R2" title="INT_1:pred.2">divides</a> <font color="Maroon" title="c2">b</font> )
 <b>and </b><br/><a NAME="E4:16_1_2"/><i><font color="Green" title="E18">A23</font></i>: 
for <font color="Olive" title="b1">m</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>  st <font color="Olive" title="b1">m</font> <a href="int_1.html#R2" title="INT_1:pred.2">divides</a> <font color="Maroon" title="c1">a</font> &amp; <font color="Olive" title="b1">m</font> <a href="int_1.html#R2" title="INT_1:pred.2">divides</a> <font color="Maroon" title="c2">b</font> holds <br/><font color="Olive" title="b1">m</font> <a href="int_1.html#R2" title="INT_1:pred.2">divides</a> <font color="Maroon" title="c4">IT2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">IT1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">IT2</font></span><br/>

<a NAME="E5:16_1_2"/>
( <font color="Maroon" title="c3">IT1</font> <a href="int_1.html#R2" title="INT_1:pred.2">divides</a> <font color="Maroon" title="c4">IT2</font> &amp; <font color="Maroon" title="c4">IT2</font> <a href="int_1.html#R2" title="INT_1:pred.2">divides</a> <font color="Maroon" title="c3">IT1</font> )
 
<b>by </b><i><a class="txt" href="#E1:16_1_2"><i><font color="Green" title="E15">A20</font></i></a>, <a class="txt" href="#E2:16_1_2"><i><font color="Green" title="E16">A21</font></i></a>, <a class="txt" href="#E3:16_1_2"><i><font color="Green" title="E17">A22</font></i></a>, <a class="txt" href="#E4:16_1_2"><i><font color="Green" title="E18">A23</font></i></a></i>;<br/>
<b>hence </b><a NAME="E6:16_1_2"/>
<font color="Maroon" title="c3">IT1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">IT2</font>
 <b>by </b><i><a class="txt" href="int_2.html#E11"><i><font color="Green" title="E11">Lm8</font></i></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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