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<b>let </b><font color="Maroon">t1</font> be   <a href="nat_1.html#NM1">Nat</a>, <font color="Maroon">t2</font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:32_1_2"/><i><font color="Green">E31</font></i>: 
(  ex <font color="Olive">t</font> being  <a href="nat_1.html#NM1">Nat</a> st <br/>( <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">l</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">t1</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Olive">t</font> &amp; <font color="Olive">t</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">l</font> ) or ( <font color="Maroon">t1</font> <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">l</font> <a href="hidden.html#R1">=</a> 0 ) )
 <b>and </b><br/><a NAME="E2:32_1_2"/><i><font color="Green">E32</font></i>: 
(  ex <font color="Olive">t</font> being  <a href="nat_1.html#NM1">Nat</a> st <br/>( <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">l</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">t2</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Olive">t</font> &amp; <font color="Olive">t</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">l</font> ) or ( <font color="Maroon">t2</font> <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">l</font> <a href="hidden.html#R1">=</a> 0 ) )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="32_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">t</font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:32_1_2_1"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">t</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0
 ;<br/><a NAME="E2:32_1_2_1"/><b>then </b>
 ex <font color="Olive">m</font> being  <a href="nat_1.html#NM1">Nat</a> st 0 <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="xcmplx_0.html#K2">+</a> <font color="Olive">m</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E3:32_1_2_1"/>
contradiction
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:32_1_2"/>
<font color="Maroon">t1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t2</font>
 <b>by </b><i>, , </i>;<br/>


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