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<span class="kw">let </span><font color="Maroon" title="c1">p</font> be  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <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> ; <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">M</font> being non  <a href="relat_1.html#V3" title="RELAT_1:attr.3">empty-yielding</a>   <a href="matrprob.html#V6" title="MATRPROB:attr.6">Conditional_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>   st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">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> <font color="Olive" title="b1">M</font> holds <br/> <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="entropy1.html#K1" title="ENTROPY1:func.1">Vec2DiagMx</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="matrixr1.html#K6" title="MATRIXR1:func.6">*</a> <font color="Olive" title="b1">M</font></span>)</span> is  <a href="matrprob.html#V1" title="MATRPROB:attr.1">ProbFinS</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">M</font> be  non  <a href="relat_1.html#V3" title="RELAT_1:attr.3">empty-yielding</a>   <a href="matrprob.html#V6" title="MATRPROB:attr.6">Conditional_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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">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> <font color="Maroon" title="c2">M</font> implies  <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="entropy1.html#K1" title="ENTROPY1:func.1">Vec2DiagMx</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="matrixr1.html#K6" title="MATRIXR1:func.6">*</a> <font color="Maroon" title="c2">M</font></span>)</span> is  <a href="matrprob.html#V1" title="MATRPROB:attr.1">ProbFinS</a>  )</span><br/>



<span class="kw">assume </span><a NAME="E1:56"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">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> <font color="Maroon" title="c2">M</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <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="entropy1.html#K1" title="ENTROPY1:func.1">Vec2DiagMx</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="matrixr1.html#K6" title="MATRIXR1:func.6">*</a> <font color="Maroon" title="c2">M</font></span>)</span> is  <a href="matrprob.html#V1" title="MATRPROB:attr.1">ProbFinS</a> </span><br/>

<a NAME="E2:56"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="entropy1.html#K1" title="ENTROPY1:func.1">Vec2DiagMx</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="matrixr1.html#K6" title="MATRIXR1:func.6">*</a> <font color="Maroon" title="c2">M</font> is   <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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="entropy1.html#T28" target="_self" title="ENTROPY1:th.28">Th28</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:56"/>
 <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="entropy1.html#K1" title="ENTROPY1:func.1">Vec2DiagMx</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="matrixr1.html#K6" title="MATRIXR1:func.6">*</a> <font color="Maroon" title="c2">M</font></span>)</span> is  <a href="matrprob.html#V1" title="MATRPROB:attr.1">ProbFinS</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="entropy1.html#T44" target="_self" title="ENTROPY1:th.44">Th44</a></span>; <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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