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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be  <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>

<a NAME="E1:59"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is   <a href="nat_1.html#NM1">Nat</a>
 
<b>by </b><i><a class="ref" href="ordinal1.html#D13">ORDINAL1:def 13</a></i>;<br/>
<b>assume </b><b>that </b><br/><a NAME="E2:59"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 <b>and </b><br/><a NAME="E3:59"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K4" target="_self">mod</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 0
 <b>and </b><br/><a NAME="E4:59"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<a NAME="E5:59"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <br/>( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K3">*</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 0 &amp; 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="txt" href="nat_1.html#E2:59"><i><font color="Green">E33</font></i></a>, <a class="txt" href="nat_1.html#E3:59"><i><font color="Green">E34</font></i></a>, <a class="ref" href="nat_1.html#D2" target="_self">Def2</a></i>;<br/>
<b>hence </b><a NAME="E6:59"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K4" target="_self">mod</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="nat_1.html#E1:59"><i><font color="Green">E32</font></i></a>, <a class="txt" href="nat_1.html#E4:59"><i><font color="Green">E35</font></i></a>, <a class="ref" href="nat_1.html#D2" target="_self">Def2</a></i>;<br/>


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