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



<a NAME="E1:104"/><i><font color="Green">E65</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K5">"</a>  <a href="hidden.html#R1">=</a> 1 <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K5">"</a>  <a href="hidden.html#R1">=</a> 1 <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="xcmplx_1.html#T217">XCMPLX_1:217</a></i>;<br/>
<b>assume </b><a NAME="E2:104"/><i><font color="Green">E66</font></i>: 
( 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/>

<a NAME="E3:104"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K5">"</a>  <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="txt" href="xreal_1.html#E129"><i><font color="Green">Lemma63</font></i></a>, <a class="txt" href="xreal_1.html#E1:104"><i><font color="Green">E65</font></i></a></i>;<br/>
<a NAME="E4:104"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K5">"</a> </span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K5">"</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="xreal_1.html#E2:104"><i><font color="Green">E66</font></i></a>, <a class="txt" href="xreal_1.html#E21"><i><font color="Green">Lemma16</font></i></a></i>;<br/>
<a NAME="E5:104"/><b>then </b><i><font color="Green">E67</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K5">"</a> </span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1
 
<b>by </b><i><a class="txt" href="xreal_1.html#E1:104"><i><font color="Green">E65</font></i></a>, <a class="txt" href="xreal_1.html#E2:104"><i><font color="Green">E66</font></i></a>, <a class="ref" href="xcmplx_1.html#T88">XCMPLX_1:88</a></i>;<br/>
<a NAME="E6:104"/>
<font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K5">"</a>  <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="txt" href="xreal_1.html#E1:104"><i><font color="Green">E65</font></i></a>, <a class="txt" href="xreal_1.html#E2:104"><i><font color="Green">E66</font></i></a>, <a class="txt" href="xreal_1.html#E129"><i><font color="Green">Lemma63</font></i></a></i>;<br/>
<a NAME="E7:104"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K5">"</a> </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="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K5">"</a> </span>)</span></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1 <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K5">"</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="xreal_1.html#E5:104"><i><font color="Green">E67</font></i></a>, <a class="txt" href="xreal_1.html#E21"><i><font color="Green">Lemma16</font></i></a></i>;<br/>
<a NAME="E8:104"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K5">"</a> </span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K5">"</a> </span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1 <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K5">"</a> </span>)</span>
 
;<br/>
<a NAME="E9:104"/><b>then </b>
1 <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K5">"</a> </span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1 <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K5">"</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="xreal_1.html#E2:104"><i><font color="Green">E66</font></i></a>, <a class="ref" href="xcmplx_0.html#D7">XCMPLX_0:def 7</a></i>;<br/>
<b>hence </b><a NAME="E10:104"/>
<font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K5">"</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K5">"</a> 
 ;<br/>


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