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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#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>  &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#K6" title="NUMBERS:func.6">0</a>  implies  <a href="power.html#K5" title="POWER:func.5">log</a> (<font color="Maroon" title="c1">a</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="power.html#K3" title="POWER:func.3">to_power</a> <font color="Maroon" title="c3">c</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">c</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="power.html#K5" title="POWER:func.5">log</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>)</span>)</span> )</span><br/>





<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:59"/><span class="lab"><font color="Green" title="E36">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> 
 <span class="kw">and </span><br/><a NAME="E2:59"/><span class="lab"><font color="Green" title="E37">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="E3:59"/><span class="lab"><font color="Green" title="E38">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#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">  <a href="power.html#K5" title="POWER:func.5">log</a> (<font color="Maroon" title="c1">a</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="power.html#K3" title="POWER:func.3">to_power</a> <font color="Maroon" title="c3">c</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">c</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="power.html#K5" title="POWER:func.5">log</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>)</span>)</span></span><br/>

<a NAME="E4:59"/><span class="lab"><font color="Green" title="E39">A4</font></span>: 
<font color="Maroon" title="c2">b</font> <a href="power.html#K3" title="POWER:func.3">to_power</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#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:59"><span class="lab"><font color="Green" title="E38">A3</font></span></a>, <a class="ref" href="power.html#T34" target="_self" title="POWER:th.34">Th39</a></span>;<br/>
<font color="Maroon" title="c1">a</font> <a href="power.html#K3" title="POWER:func.3">to_power</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">c</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="power.html#K5" title="POWER:func.5">log</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>)</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="power.html#K3" title="POWER:func.3">to_power</a> <span class="p2">(<span class="default"><a href="power.html#K5" title="POWER:func.5">log</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>)</span>)</span></span>)</span> <a href="power.html#K3" title="POWER:func.3">to_power</a> <font color="Maroon" title="c3">c</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:59"><span class="lab"><font color="Green" title="E36">A1</font></span></a>, <a class="ref" href="power.html#T33" target="_self" title="POWER:th.33">Th38</a></span>
<br/>.= 
<font color="Maroon" title="c2">b</font> <a href="power.html#K3" title="POWER:func.3">to_power</a> <font color="Maroon" title="c3">c</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:59"><span class="lab"><font color="Green" title="E36">A1</font></span></a>, <a class="txt" href="#E2:59"><span class="lab"><font color="Green" title="E37">A2</font></span></a>, <a class="txt" href="#E3:59"><span class="lab"><font color="Green" title="E38">A3</font></span></a>, <a class="ref" href="power.html#D3" target="_self" title="POWER:def.3">Def3</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E6:59"/>
 <a href="power.html#K5" title="POWER:func.5">log</a> (<font color="Maroon" title="c1">a</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="power.html#K3" title="POWER:func.3">to_power</a> <font color="Maroon" title="c3">c</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">c</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="power.html#K5" title="POWER:func.5">log</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:59"><span class="lab"><font color="Green" title="E36">A1</font></span></a>, <a class="txt" href="#E2:59"><span class="lab"><font color="Green" title="E37">A2</font></span></a>, <a class="txt" href="#E4:59"><span class="lab"><font color="Green" title="E39">A4</font></span></a>, <a class="ref" href="power.html#D3" target="_self" title="POWER:def.3">Def3</a></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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