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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E27">Th21</font></span>: <a NAME="T21"><span class="comment"><font color="firebrick">:: HUFFMAN1:21</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">SOURCE</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">p</font> being    <a href="prob_1.html#M2" title="PROB_1:mode.2">Probability</a> of  <a href="random_1.html#K1" title="RANDOM_1:func.1">Trivial-SigmaField</a> <font color="Olive" title="b1">SOURCE</font><br/>  for <font color="Olive" title="b3">Tseq</font> being    <a href="trees_4.html#M1" title="TREES_4:mode.1">FinSequence</a> of  <a href="huffman1.html#K3" title="HUFFMAN1:func.3">BoolBinFinTrees</a> <a href="huffman1.html#K1" title="HUFFMAN1:func.1">IndexedREAL</a><br/>  for <font color="Olive" title="b4">q</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>   st <font color="Olive" title="b3">Tseq</font>,<font color="Olive" title="b4">q</font>,<font color="Olive" title="b2">p</font> <a href="huffman1.html#R1" title="HUFFMAN1:pred.1">is_constructingBinHuffmanTree</a>  holds <br/> for <font color="Olive" title="b5">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b6">T</font> being   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>   <a href="bintree1.html#V2" title="BINTREE1:attr.2">binary</a>  <a href="trees_2.html#NM5" title="TREES_2:NM.5">DecoratedTree</a> of  <a href="huffman1.html#K1" title="HUFFMAN1:func.1">IndexedREAL</a> <br/>  for <font color="Olive" title="b7">t</font>, <font color="Olive" title="b8">s</font>, <font color="Olive" title="b9">r</font> being    <a href="trees_1.html#M1" title="TREES_1:mode.1">Element</a> of  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b6">T</font>  st <font color="Olive" title="b6">T</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">Tseq</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">i</font> &amp; <font color="Olive" title="b7">t</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b6">T</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><a href="trees_1.html#K3" title="TREES_1:func.3">Leaves</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b6">T</font></span>)</span></span>)</span> &amp; <font color="Olive" title="b8">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b7">t</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="trees_3.html#K14" title="TREES_3:func.14">&lt;*</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="trees_3.html#K14" title="TREES_3:func.14">*&gt;</a></span> &amp; <font color="Olive" title="b9">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b7">t</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="trees_3.html#K14" title="TREES_3:func.14">&lt;*</a><span class="default">1</span><a href="trees_3.html#K14" title="TREES_3:func.14">*&gt;</a></span> holds <br/> <a href="huffman1.html#K7" title="HUFFMAN1:func.7">Vtree</a> <font color="Olive" title="b7">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="huffman1.html#K7" title="HUFFMAN1:func.7">Vtree</a> <font color="Olive" title="b8">s</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="huffman1.html#K7" title="HUFFMAN1:func.7">Vtree</a> <font color="Olive" title="b9">r</font></span>)</span></div></div>
