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<b>let </b><font color="Maroon" title="c1">m</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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( 2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">m</font> implies 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 2 )</span><br/>

<b>assume </b><a NAME="E1:13"/><i><font color="Green" title="E14">A1</font></i>: 
2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">m</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 2</span><br/>

<a NAME="E2:13"/><b>then </b>
2 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 2 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c1">m</font>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T68" title="XREAL_1:th.68">XREAL_1:68</a></i>;<br/>
<a NAME="E3:13"/><b>then </b><i><font color="Green" title="E15">A2</font></i>: 
4 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 2
 
<b>by </b><i><a class="ref" href="xreal_1.html#T11" title="XREAL_1:th.11">XREAL_1:11</a></i>;<br/>
<a NAME="E4:13"/>
<span class="p1">(<span class="default">2 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 2 <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="c1">m</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 2
 
<b>by </b><i><a class="txt" href="jordan1d.html#E1:13"><i><font color="Green" title="E14">A1</font></i></a>, <a class="txt" href="jordan1d.html#E15"><i><font color="Green" title="E9">Lm7</font></i></a></i>;<br/>
<b>hence </b><a NAME="E5:13"/>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 2
 <b>by </b><i><a class="txt" href="jordan1d.html#E3:13"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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