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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E34">Th30</font></span>: <a NAME="T30"><span class="comment"><font color="firebrick">:: HUFFMAN1:30</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</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="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="huffman1.html#K2" title="HUFFMAN1:func.2">BinFinTrees</a> <a href="huffman1.html#K1" title="HUFFMAN1:func.1">IndexedREAL</a></span>)</span><br/>  for <font color="Olive" title="b2">s</font>, <font color="Olive" title="b3">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>   st <font color="Olive" title="b2">s</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  &amp; <font color="Olive" title="b3">t</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  &amp; <font color="Olive" title="b3">t</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">X</font> &amp; <font color="Olive" title="b2">s</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">X</font> &amp; <span class="p1">(<span class="default"><a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Olive" title="b2">s</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Olive" title="b3">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; (  for <font color="Olive" title="b4">z</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>   st <font color="Olive" title="b4">z</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">X</font> holds <br/> not <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="huffman1.html#K9" title="HUFFMAN1:func.9">MaxVl</a> <font color="Olive" title="b1">X</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="huffman1.html#K5" title="HUFFMAN1:func.5">Vrootr</a> <font color="Olive" title="b3">t</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><a href="huffman1.html#K5" title="HUFFMAN1:func.5">Vrootr</a> <font color="Olive" title="b2">s</font></span>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Olive" title="b4">z</font> ) holds <br/> <a href="huffman1.html#K8" title="HUFFMAN1:func.8">MakeTree</a> (<font color="Olive" title="b3">t</font>,<font color="Olive" title="b2">s</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="huffman1.html#K9" title="HUFFMAN1:func.9">MaxVl</a> <font color="Olive" title="b1">X</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>) is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a> </div></div>
