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<b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:62_1_2"/><i><font color="Green">E49</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="nat_1.html#K4">mod</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 1 &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="wsierp_1.html#K2">|^</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="nat_1.html#K4">mod</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 1 holds <br/>( 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> ) ) )
 <b>and </b><br/><a NAME="E2:62_1_2"/><i><font color="Green">E50</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nat_1.html#K4">mod</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 1 &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="wsierp_1.html#K2">|^</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="nat_1.html#K4">mod</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 1 holds <br/>( 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> ) ) )
 ;<br/>

<a NAME="E3:62_1_2"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="txt" href="pepin.html#E1:62_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="pepin.html#E2:62_1_2"><i><font color="Green">E50</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:62_1_2"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/>


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