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<span class="kw">let </span><font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c2">b</font>, <font color="Maroon" title="c3">c</font> be   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Maroon" title="c1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 &amp; <font color="Maroon" title="c2">b</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Maroon" title="c3">c</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  implies <span class="p1">(<span class="default"><a href="power.html#K3" title="POWER:func.3">log</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>)</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="power.html#K3" title="POWER:func.3">log</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">c</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="power.html#K3" title="POWER:func.3">log</a> (<font color="Maroon" title="c1">a</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c3">c</font></span>)</span>) )</span><br/>





<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:55"/><span class="lab"><font color="Green" title="E35">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#K5" title="NUMBERS:func.5">0</a> 
 <span class="kw">and </span><br/><a NAME="E2:55"/><span class="lab"><font color="Green" title="E36">A2</font></span>: 
<font color="Maroon" title="c1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1
 <span class="kw">and </span><br/><a NAME="E3:55"/><span class="lab"><font color="Green" title="E37">A3</font></span>: 
<font color="Maroon" title="c2">b</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 <span class="kw">and </span><br/><a NAME="E4:55"/><span class="lab"><font color="Green" title="E38">A4</font></span>: 
<font color="Maroon" title="c3">c</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="power.html#K3" title="POWER:func.3">log</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>)</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="power.html#K3" title="POWER:func.3">log</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">c</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="power.html#K3" title="POWER:func.3">log</a> (<font color="Maroon" title="c1">a</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c3">c</font></span>)</span>)</span><br/>

<span class="lab"><font color="Green" title="E39">A5</font></span>: <font color="Maroon" title="c1">a</font> <a href="power.html#K2" title="POWER:func.2">to_power</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="power.html#K3" title="POWER:func.3">log</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>)</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><a href="power.html#K3" title="POWER:func.3">log</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">c</font>)</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="power.html#K2" title="POWER:func.2">to_power</a> <span class="p2">(<span class="default"><a href="power.html#K3" title="POWER:func.3">log</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="power.html#K2" title="POWER:func.2">to_power</a> <span class="p2">(<span class="default"><a href="power.html#K3" title="POWER:func.3">log</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">c</font>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:55"><span class="lab"><font color="Green" title="E35">A1</font></span></a>, <a class="ref" href="power.html#T29" target="_self" onmouseover="rs('power/T29')" onmouseout="rh()">Th29</a></span>
<br/>.= 
<font color="Maroon" title="c2">b</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="power.html#K2" title="POWER:func.2">to_power</a> <span class="p2">(<span class="default"><a href="power.html#K3" title="POWER:func.3">log</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">c</font>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:55"><span class="lab"><font color="Green" title="E35">A1</font></span></a>, <a class="txt" href="#E2:55"><span class="lab"><font color="Green" title="E36">A2</font></span></a>, <a class="txt" href="#E3:55"><span class="lab"><font color="Green" title="E37">A3</font></span></a>, <a class="ref" href="power.html#D3" target="_self" onmouseover="rs('power/D3')" onmouseout="rh()">Def3</a></span>
<br/>.= 
<font color="Maroon" title="c2">b</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c3">c</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:55"><span class="lab"><font color="Green" title="E35">A1</font></span></a>, <a class="txt" href="#E2:55"><span class="lab"><font color="Green" title="E36">A2</font></span></a>, <a class="txt" href="#E4:55"><span class="lab"><font color="Green" title="E38">A4</font></span></a>, <a class="ref" href="power.html#D3" target="_self" onmouseover="rs('power/D3')" onmouseout="rh()">Def3</a></span>
;<br/>
<a NAME="E6:55"/>
<font color="Maroon" title="c2">b</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c3">c</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:55"><span class="lab"><font color="Green" title="E37">A3</font></span></a>, <a class="txt" href="#E4:55"><span class="lab"><font color="Green" title="E38">A4</font></span></a>, <a class="ref" href="xreal_1.html#T139" onmouseover="rs('xreal_1/T139')" onmouseout="rh()">XREAL_1:139</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:55"/>
<span class="p1">(<span class="default"><a href="power.html#K3" title="POWER:func.3">log</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>)</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="power.html#K3" title="POWER:func.3">log</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">c</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="power.html#K3" title="POWER:func.3">log</a> (<font color="Maroon" title="c1">a</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c3">c</font></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:55"><span class="lab"><font color="Green" title="E35">A1</font></span></a>, <a class="txt" href="#E2:55"><span class="lab"><font color="Green" title="E36">A2</font></span></a>, <a class="txt" href="#E5:55"><span class="lab"><font color="Green" title="E39">A5</font></span></a>, <a class="ref" href="power.html#D3" target="_self" onmouseover="rs('power/D3')" onmouseout="rh()">Def3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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