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<b>let </b><font color="Maroon" title="c2">n1</font>, <font color="Maroon" title="c3">m1</font>, <font color="Maroon" title="c4">n2</font>, <font color="Maroon" title="c5">m2</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>







<b>assume </b><a NAME="E1:42"/><i><font color="Green" title="E31">A1</font></i>: 
<span class="p1">(<span class="default">2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> <font color="Maroon" title="c2">n1</font></span>)</span> <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c3">m1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> <font color="Maroon" title="c4">n2</font></span>)</span> <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c5">m2</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 ;<br/>

<a NAME="E2:42"/><b>then </b>
( <font color="Maroon" title="c2">n1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">n2</font> &amp; <font color="Maroon" title="c4">n2</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">n1</font> )
 
<b>by </b><i><a class="txt" href="card_4.html#E55"><i><font color="Green" title="E29">Lm3</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:42"/><i><font color="Green" title="E32">A2</font></i>: 
<font color="Maroon" title="c2">n1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">n2</font>
 <b>by </b><i><a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/>

<a NAME="E4:42"/>
2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> <font color="Maroon" title="c2">n1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="ref" href="card_4.html#T51" target="_self" title="CARD_4:th.51">Th51</a></i>;<br/>
<a NAME="E5:42"/><b>then </b>
<span class="p1">(<span class="default">2 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c3">m1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c5">m2</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 
<b>by </b><i><a class="txt" href="card_4.html#E1:42"><i><font color="Green" title="E31">A1</font></i></a>, <a class="txt" href="card_4.html#E3:42"><i><font color="Green" title="E32">A2</font></i></a>, <a class="ref" href="xcmplx_1.html#T5" title="XCMPLX_1:th.5">XCMPLX_1:5</a></i>;<br/>
<b>hence </b><a NAME="E6:42"/>
<font color="Maroon" title="c3">m1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">m2</font>
 ;<br/>


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