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<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c3">b</font>, <font color="Maroon" title="c4">c</font> be  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ;<br/><b>assume </b><b>that </b><br/><a NAME="E1:24_1_2_1"/><i><font color="Green" title="E19">A47</font></i>: 
( <font color="Maroon" title="c3">b</font> <a href="newton.html#K2" title="NEWTON:func.2">|^</a> <font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> &amp; <font color="Maroon" title="c3">b</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0 )
 <b>and </b><br/><a NAME="E2:24_1_2_1"/><i><font color="Green" title="E20">A48</font></i>: 
( <font color="Maroon" title="c4">c</font> <a href="newton.html#K2" title="NEWTON:func.2">|^</a> <font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> &amp; <font color="Maroon" title="c4">c</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0 )
 <b>and </b><br/><a NAME="E3:24_1_2_1"/><i><font color="Green" title="E21">A49</font></i>: 
<font color="Maroon" title="c3">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">c</font>
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:24_1_2_1_1"/>
( <font color="Maroon" title="c3">b</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c4">c</font> or <font color="Maroon" title="c4">c</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c3">b</font> )
 </span><b>by </b><i><a class="txt" href="prepower.html#E3:24_1_2_1"><i><font color="Green" title="E21">A49</font></i></a>, <a class="ref" href="real_1.html#D5" title="REAL_1:def.5">REAL_1:def 5</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_1_2_1_1_1"><b>suppose </b></a><a NAME="E1:24_1_2_1_1_1"/>
<font color="Maroon" title="c3">b</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c4">c</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:24_1_2_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="prepower.html#E1:24"><i><font color="Green" title="E18">A1</font></i></a>, <a class="txt" href="prepower.html#E1:24_1_2_1"><i><font color="Green" title="E19">A47</font></i></a>, <a class="txt" href="prepower.html#E2:24_1_2_1"><i><font color="Green" title="E20">A48</font></i></a>, <a class="txt" href="prepower.html#E20"><i><font color="Green" title="E10">Lm2</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_1_2_1_1_2"><b>suppose </b></a><a NAME="E1:24_1_2_1_1_2"/>
<font color="Maroon" title="c4">c</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c3">b</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:24_1_2_1_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="prepower.html#E1:24"><i><font color="Green" title="E18">A1</font></i></a>, <a class="txt" href="prepower.html#E1:24_1_2_1"><i><font color="Green" title="E19">A47</font></i></a>, <a class="txt" href="prepower.html#E2:24_1_2_1"><i><font color="Green" title="E20">A48</font></i></a>, <a class="txt" href="prepower.html#E20"><i><font color="Green" title="E10">Lm2</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E2:24_1_2"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>  holds <br/> ( ( <font color="Maroon" title="c2">a</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0 &amp; <font color="Olive">b<sub>1</sub></font> <a href="newton.html#K2" title="NEWTON:func.2">|^</a> <font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0 &amp; <font color="Olive">b<sub>2</sub></font> <a href="newton.html#K2" title="NEWTON:func.2">|^</a> <font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0 implies <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>2</sub></font> ) &amp; ( <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 implies <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>2</sub></font> ) )
 ;<br/>


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