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<span class="kw">let </span><font color="Maroon" title="c1">r1</font>, <font color="Maroon" title="c2">r2</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">p</font> being  <a href="partfun3.html#V4" title="PARTFUN3:attr.4">nonnegative</a>   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>   st <font color="Maroon" title="c1">r1</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c2">r2</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  holds <br/>for <font color="Olive" title="b2">i</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Olive" title="b2">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Olive" title="b1">p</font> &amp; <font color="Olive" title="b1">p</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">r1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c2">r2</font> holds <br/><span class="p1">(<span class="default"><a href="entropy1.html#K4" title="ENTROPY1:func.4">Infor_FinSeq_of</a> <font color="Olive" title="b1">p</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">r1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c2">r2</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c1">r1</font></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">r1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c2">r2</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c2">r2</font></span>)</span></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">p</font> be   <a href="partfun3.html#V4" title="PARTFUN3:attr.4">nonnegative</a>   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">r1</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c2">r2</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies for <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Olive" title="b1">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c3">p</font> &amp; <font color="Maroon" title="c3">p</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">r1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c2">r2</font> holds <br/><span class="p1">(<span class="default"><a href="entropy1.html#K4" title="ENTROPY1:func.4">Infor_FinSeq_of</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">r1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c2">r2</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c1">r1</font></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">r1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c2">r2</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c2">r2</font></span>)</span></span>)</span> )</span><br/>





<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:62"/><span class="lab"><font color="Green" title="E53">A1</font></span>: 
<font color="Maroon" title="c1">r1</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">and </span><br/><a NAME="E2:62"/><span class="lab"><font color="Green" title="E54">A2</font></span>: 
<font color="Maroon" title="c2">r2</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&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="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Olive" title="b1">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c3">p</font> &amp; <font color="Maroon" title="c3">p</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">r1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c2">r2</font> holds <br/><span class="p1">(<span class="default"><a href="entropy1.html#K4" title="ENTROPY1:func.4">Infor_FinSeq_of</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">r1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c2">r2</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c1">r1</font></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">r1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c2">r2</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c2">r2</font></span>)</span></span>)</span></span><br/>

<span class="kw">let </span><font color="Maroon" title="c4">i</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c3">p</font> &amp; <font color="Maroon" title="c3">p</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">r1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c2">r2</font> implies <span class="p1">(<span class="default"><a href="entropy1.html#K4" title="ENTROPY1:func.4">Infor_FinSeq_of</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">r1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c2">r2</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c1">r1</font></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">r1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c2">r2</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c2">r2</font></span>)</span></span>)</span> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E3:62"/><span class="lab"><font color="Green" title="E55">A3</font></span>: 
<font color="Maroon" title="c4">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c3">p</font>
 <span class="kw">and </span><br/><a NAME="E4:62"/><span class="lab"><font color="Green" title="E56">A4</font></span>: 
<font color="Maroon" title="c3">p</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">r1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c2">r2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="entropy1.html#K4" title="ENTROPY1:func.4">Infor_FinSeq_of</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">r1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c2">r2</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c1">r1</font></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">r1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c2">r2</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c2">r2</font></span>)</span></span>)</span></span><br/>

<a NAME="E5:62"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="entropy1.html#K4" title="ENTROPY1:func.4">Infor_FinSeq_of</a> <font color="Maroon" title="c3">p</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="entropy1.html#T47" target="_self" title="ENTROPY1:th.47">Th47</a></span>;<br/>
<a NAME="E6:62"/><span class="kw">then </span>
<font color="Maroon" title="c4">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="entropy1.html#K4" title="ENTROPY1:func.4">Infor_FinSeq_of</a> <font color="Maroon" title="c3">p</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:62"><span class="lab"><font color="Green" title="E55">A3</font></span></a>, <a class="ref" href="finseq_3.html#T31" title="FINSEQ_3:th.31">FINSEQ_3:31</a></span>;<br/>
<span class="kw">hence </span><span class="p1">(<span class="default"><a href="entropy1.html#K4" title="ENTROPY1:func.4">Infor_FinSeq_of</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">i</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">r1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c2">r2</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<span class="p2">(<span class="default"><font color="Maroon" title="c1">r1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c2">r2</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:62"><span class="lab"><font color="Green" title="E56">A4</font></span></a>, <a class="ref" href="entropy1.html#T47" target="_self" title="ENTROPY1:th.47">Th47</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">r1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c2">r2</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c1">r1</font></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">r1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c2">r2</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><a href="power.html#K6" title="POWER:func.6">log</a> 2,<font color="Maroon" title="c2">r2</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:62"><span class="lab"><font color="Green" title="E53">A1</font></span></a>, <a class="txt" href="#E2:62"><span class="lab"><font color="Green" title="E54">A2</font></span></a>, <a class="ref" href="entropy1.html#T6" target="_self" title="ENTROPY1:th.6">Th6</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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