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<span class="kw">let </span><font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c2">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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies <span class="p1">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="prepower.html#K9" title="PREPOWER:func.9">#R</a> <font color="Maroon" title="c2">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K9" title="PREPOWER:func.9">#R</a> <font color="Maroon" title="c2">c</font></span>)</span> )</span><br/>



<span class="kw">assume </span><a NAME="E1:104"/><span class="lab"><font color="Green" title="E85">A1</font></span>: 
<font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="prepower.html#K9" title="PREPOWER:func.9">#R</a> <font color="Maroon" title="c2">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K9" title="PREPOWER:func.9">#R</a> <font color="Maroon" title="c2">c</font></span>)</span></span><br/>

1 = 
1 <a href="prepower.html#K9" title="PREPOWER:func.9">#R</a> <font color="Maroon" title="c2">c</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="prepower.html#T73" target="_self" title="PREPOWER:th.73">Th87</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="prepower.html#K9" title="PREPOWER:func.9">#R</a> <font color="Maroon" title="c2">c</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:104"><span class="lab"><font color="Green" title="E85">A1</font></span></a>, <a class="ref" href="xcmplx_1.html#T106" title="XCMPLX_1:th.106">XCMPLX_1:106</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="prepower.html#K9" title="PREPOWER:func.9">#R</a> <font color="Maroon" title="c2">c</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K9" title="PREPOWER:func.9">#R</a> <font color="Maroon" title="c2">c</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:104"><span class="lab"><font color="Green" title="E85">A1</font></span></a>, <a class="ref" href="prepower.html#T78" target="_self" title="PREPOWER:th.78">Th92</a></span>
;<br/>
<span class="kw">then </span>1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K9" title="PREPOWER:func.9">#R</a> <font color="Maroon" title="c2">c</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="prepower.html#K9" title="PREPOWER:func.9">#R</a> <font color="Maroon" title="c2">c</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K9" title="PREPOWER:func.9">#R</a> <font color="Maroon" title="c2">c</font></span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K9" title="PREPOWER:func.9">#R</a> <font color="Maroon" title="c2">c</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xcmplx_1.html#T74" title="XCMPLX_1:th.74">XCMPLX_1:74</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="prepower.html#K9" title="PREPOWER:func.9">#R</a> <font color="Maroon" title="c2">c</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> 1
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:104"><span class="lab"><font color="Green" title="E85">A1</font></span></a>, <a class="txt" href="prepower.html#E91"><span class="lab"><font color="Green" title="E80">Lm9</font></span></a>, <a class="ref" href="xcmplx_1.html#T60" title="XCMPLX_1:th.60">XCMPLX_1:60</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E4:104"/>
<span class="p1">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="prepower.html#K9" title="PREPOWER:func.9">#R</a> <font color="Maroon" title="c2">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K9" title="PREPOWER:func.9">#R</a> <font color="Maroon" title="c2">c</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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