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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be  <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:123"/><i><font color="Green">E98</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E2:123"/><i><font color="Green">E99</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>4</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E4:123"/><i><font color="Green">E100</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="prepower.html#E1:123"><i><font color="Green">E98</font></i></a>, <a class="ref" href="nat_1.html#T28">NAT_1:28</a></i>;<br/>
<a NAME="E5:123"/><i><font color="Green">E101</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="newton.html#K2">|^</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="newton.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="newton.html#K2">|^</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="prepower.html#E4:123"><i><font color="Green">E100</font></i></a>, <a class="ref" href="newton.html#T13">NEWTON:13</a></i>;<br/>
<a NAME="E6:123"/>
<font color="Maroon">c<sub>2</sub></font> <a href="newton.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 
<b>by </b><i><a class="txt" href="prepower.html#E2:123"><i><font color="Green">E99</font></i></a>, <a class="ref" href="prepower.html#T19" target="_self">Th19</a></i>;<br/>
<a NAME="E7:123"/><b>then </b><i><font color="Green">E102</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="newton.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 
;<br/>
<a NAME="E8:123"/>
<font color="Maroon">c<sub>2</sub></font> <a href="newton.html#K2">|^</a> <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 
<b>by </b><i><a class="txt" href="prepower.html#E2:123"><i><font color="Green">E99</font></i></a>, <a class="ref" href="prepower.html#T19" target="_self">Th19</a></i>;<br/>
<b>hence </b><a NAME="E9:123"/>
<font color="Maroon">c<sub>2</sub></font> <a href="newton.html#K2">|^</a> <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>2</sub></font> <a href="newton.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="prepower.html#E5:123"><i><font color="Green">E101</font></i></a>, <a class="txt" href="prepower.html#E7:123"><i><font color="Green">E102</font></i></a>, <a class="ref" href="real_2.html#T146">REAL_2:146</a></i>;<br/>


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