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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E7">Th10</font></span>: <a NAME="T10"><span class="comment"><font color="firebrick">:: BINTREE1:10</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">G</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="dtconstr.html#V1" title="DTCONSTR:attr.1">with_terminals</a>   <a href="dtconstr.html#V2" title="DTCONSTR:attr.2">with_nonterminals</a>   <a href="bintree1.html#V3" title="BINTREE1:attr.3">binary</a>   <a href="lang1.html#L1" title="LANG1:struct.1">DTConstrStr</a> <br/>  for <font color="Olive" title="b2">ts</font> being    <a href="trees_4.html#M1" title="TREES_4:mode.1">FinSequence</a> of  <a href="dtconstr.html#K4" title="DTCONSTR:func.4">TS</a> <font color="Olive" title="b1">G</font><br/>  for <font color="Olive" title="b3">nt</font> being   <a href="lang1.html#NM1" title="LANG1:NM.1">Symbol</a> of <font color="Olive" title="b1">G</font>  st <font color="Olive" title="b3">nt</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a>  <a href="dtconstr.html#K1" title="DTCONSTR:func.1">roots</a> <font color="Olive" title="b2">ts</font> holds <br/>( <font color="Olive" title="b3">nt</font> is   <a href="dtconstr.html#NM3" title="DTCONSTR:NM.3">NonTerminal</a> of <font color="Olive" title="b1">G</font> &amp;  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Olive" title="b2">ts</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">1,2</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp; 1 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Olive" title="b2">ts</font> &amp; 2 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Olive" title="b2">ts</font> &amp;  ex <font color="Olive" title="b4">tl</font>, <font color="Olive" title="b5">tr</font> being    <a href="dtconstr.html#M1" title="DTCONSTR:mode.1">Element</a> of  <a href="dtconstr.html#K4" title="DTCONSTR:func.4">TS</a> <font color="Olive" title="b1">G</font> st <br/>(  <a href="dtconstr.html#K1" title="DTCONSTR:func.1">roots</a> <font color="Olive" title="b2">ts</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="pre_poly.html#K4" title="PRE_POLY:func.4">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="bintree1.html#K1" title="BINTREE1:func.1">root-label</a> <font color="Olive" title="b4">tl</font></span>)</span>,<span class="p2">(<span class="default"><a href="bintree1.html#K1" title="BINTREE1:func.1">root-label</a> <font color="Olive" title="b5">tr</font></span>)</span></span><a href="pre_poly.html#K4" title="PRE_POLY:func.4">*&gt;</a></span> &amp; <font color="Olive" title="b4">tl</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">ts</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 &amp; <font color="Olive" title="b5">tr</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">ts</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 &amp; <font color="Olive" title="b3">nt</font> <a href="trees_4.html#K8" title="TREES_4:func.8">-tree</a> <font color="Olive" title="b2">ts</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">nt</font> <a href="trees_4.html#K6" title="TREES_4:func.6">-tree</a> (<font color="Olive" title="b4">tl</font>,<font color="Olive" title="b5">tr</font>) &amp; <font color="Olive" title="b4">tl</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Olive" title="b2">ts</font> &amp; <font color="Olive" title="b5">tr</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Olive" title="b2">ts</font> ) )</div></div>
