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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>



<b>assume </b><a NAME="E1:55"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="binarith.html#K5" target="_self">-'</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 0
 ;<br/>

<b>assume </b><a NAME="E2:55"/>
<font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<a NAME="E3:55"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="binop_2.html#K23">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E4:55"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="binop_2.html#K23">+</a> 1</span>)</span> <a href="binop_2.html#K10">-</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font> <a href="binop_2.html#K10">-</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/>
<b>hence </b><a NAME="E5:55"/>
contradiction
 <b>by </b><i><a class="txt" href="binarith.html#E1:55"><i><font color="Green">E33</font></i></a>, <a class="ref" href="binarith.html#D3" target="_self">Def3</a></i>;<br/>


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