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<b>let </b><font color="Maroon" title="c1">p</font>, <font color="Maroon" title="c2">q</font> be  <a href="matrprob.html#V1" title="MATRPROB:attr.1">ProbFinS</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> ;<br/>

<b>set </b><font color="Maroon" title="c3">pp</font> =  <a href="entropy1.html#K2" title="ENTROPY1:func.2">Mx2FinS</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixr1.html#K9" title="MATRIXR1:func.9">ColVec2Mx</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="matrixr1.html#K6" title="MATRIXR1:func.6">*</a> <span class="p2">(<span class="default"><a href="matrixr1.html#K10" title="MATRIXR1:func.10">LineVec2Mx</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c4">M</font> = <span class="p1">(<span class="default"><a href="matrixr1.html#K9" title="MATRIXR1:func.9">ColVec2Mx</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="matrixr1.html#K6" title="MATRIXR1:func.6">*</a> <span class="p1">(<span class="default"><a href="matrixr1.html#K10" title="MATRIXR1:func.10">LineVec2Mx</a> <font color="Maroon" title="c2">q</font></span>)</span>;<br/>
<b>reconsider </b><font color="Maroon" title="c5">M</font> = <span class="p1">(<span class="default"><a href="matrixr1.html#K9" title="MATRIXR1:func.9">ColVec2Mx</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="matrixr1.html#K6" title="MATRIXR1:func.6">*</a> <span class="p1">(<span class="default"><a href="matrixr1.html#K10" title="MATRIXR1:func.10">LineVec2Mx</a> <font color="Maroon" title="c2">q</font></span>)</span> as  <a href="matrprob.html#V4" title="MATRPROB:attr.4">Joint_Probability</a> <a href="matrix_1.html#NM1" title="MATRIX_1:NM.1">Matrix</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  <b>by </b><i><a class="ref" href="entropy1.html#T23" target="_self" title="ENTROPY1:th.23">Th23</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">pp</font> =  <a href="entropy1.html#K2" title="ENTROPY1:func.2">Mx2FinS</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixr1.html#K9" title="MATRIXR1:func.9">ColVec2Mx</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="matrixr1.html#K6" title="MATRIXR1:func.6">*</a> <span class="p2">(<span class="default"><a href="matrixr1.html#K10" title="MATRIXR1:func.10">LineVec2Mx</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span> as  <a href="matrprob.html#V1" title="MATRPROB:attr.1">ProbFinS</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>  <b>by </b><i><a class="ref" href="entropy1.html#T45" target="_self" title="ENTROPY1:th.45">Th45</a></i>;<br/>
<span class="p1">(<span class="default"><a href="entropy1.html#K6" title="ENTROPY1:func.6">Entropy</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><a href="entropy1.html#K6" title="ENTROPY1:func.6">Entropy</a> <font color="Maroon" title="c2">q</font></span>)</span> = 
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rvsum_1.html#K18" title="RVSUM_1:func.18">Sum</a> <span class="p3">(<span class="default"><a href="entropy1.html#K4" title="ENTROPY1:func.4">Infor_FinSeq_of</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><a href="rvsum_1.html#K18" title="RVSUM_1:func.18">Sum</a> <span class="p3">(<span class="default"><a href="entropy1.html#K4" title="ENTROPY1:func.4">Infor_FinSeq_of</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span></span>)</span>

<br/>.= 
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><a href="matrprob.html#K5" title="MATRPROB:func.5">SumAll</a> <span class="p2">(<span class="default"><a href="entropy1.html#K5" title="ENTROPY1:func.5">Infor_FinSeq_of</a> <font color="Maroon" title="c5">M</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="entropy1.html#T60" target="_self" title="ENTROPY1:th.60">Th60</a></i>
<br/>.= 
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K18" title="RVSUM_1:func.18">Sum</a> <span class="p2">(<span class="default"><a href="entropy1.html#K2" title="ENTROPY1:func.2">Mx2FinS</a> <span class="p3">(<span class="default"><a href="entropy1.html#K5" title="ENTROPY1:func.5">Infor_FinSeq_of</a> <font color="Maroon" title="c5">M</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="entropy1.html#T42" target="_self" title="ENTROPY1:th.42">Th42</a></i>
<br/>.= 
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K18" title="RVSUM_1:func.18">Sum</a> <span class="p2">(<span class="default"><a href="entropy1.html#K4" title="ENTROPY1:func.4">Infor_FinSeq_of</a> <font color="Maroon" title="c6">pp</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="entropy1.html#T59" target="_self" title="ENTROPY1:th.59">Th59</a></i>
;<br/>
<b>hence </b><a NAME="E4:76"/>
 <a href="entropy1.html#K7" title="ENTROPY1:func.7">Entropy_of_Joint_Prob</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixr1.html#K9" title="MATRIXR1:func.9">ColVec2Mx</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="matrixr1.html#K6" title="MATRIXR1:func.6">*</a> <span class="p2">(<span class="default"><a href="matrixr1.html#K10" title="MATRIXR1:func.10">LineVec2Mx</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="entropy1.html#K6" title="ENTROPY1:func.6">Entropy</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><a href="entropy1.html#K6" title="ENTROPY1:func.6">Entropy</a> <font color="Maroon" title="c2">q</font></span>)</span>
 ;<br/>


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