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<span class="kw">defpred </span><font color="Maroon">S<sub>1</sub></font>[  <a href="trees_2.html#NM4" title="TREES_2:NM.4">DecoratedTree</a>] <span class="kw">means </span><font color="Maroon" title="c1">G</font> is  <a href="bintree1.html#V2" title="BINTREE1:attr.2">binary</a> ;<br/>
<div><span class="lab"><font color="Green" title="E8">A1</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="24_1_1_1"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">s</font> being   <a href="dtconstr.html#NM2" title="DTCONSTR:NM.2">Terminal</a> of <font color="Maroon" title="c1">G</font> holds  <font color="Maroon">S<sub>1</sub></font>[ <a href="dtconstr.html#K8" title="DTCONSTR:func.8">root-tree</a> <font color="Olive" title="b1">s</font>]</span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c2">s</font> be   <a href="dtconstr.html#NM2" title="DTCONSTR:NM.2">Terminal</a> of <font color="Maroon" title="c1">G</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon">S<sub>1</sub></font>[ <a href="dtconstr.html#K8" title="DTCONSTR:func.8">root-tree</a> <font color="Maroon" title="c2">s</font>]</span><br/><a NAME="E1:24_1_1_1"/>
 <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K8" title="DTCONSTR:func.8">root-tree</a> <font color="Maroon" title="c2">s</font></span>)</span> is  <a href="bintree1.html#V1" title="BINTREE1:attr.1">binary</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="trees_4.html#T3" onmouseover="rs('trees_4/T3')" onmouseout="rh()">TREES_4:3</a></span>;<br/><span class="kw">hence </span><a NAME="E2:24_1_1_1"/>
<font color="Maroon">S<sub>1</sub></font>[ <a href="dtconstr.html#K8" title="DTCONSTR:func.8">root-tree</a> <font color="Maroon" title="c2">s</font>]
 <span class="kw">by</span> <span class="lab"><a class="ref" href="bintree1.html#D3" target="_self" onmouseover="rs('bintree1/D3')" onmouseout="rh()">Def3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E2:24_1_1"/><span class="lab"><font color="Green" title="E9">A2</font></span>: 
 for <font color="Olive" title="b1">nt</font> being   <a href="dtconstr.html#NM3" title="DTCONSTR:NM.3">NonTerminal</a> of <font color="Maroon" title="c1">G</font><br/>  for <font color="Olive" title="b2">tl</font>, <font color="Olive" title="b3">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="Maroon" title="c1">G</font>  st <font color="Olive" title="b1">nt</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</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="b2">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="b3">tr</font></span>)</span></span><a href="pre_poly.html#K4" title="PRE_POLY:func.4">*&gt;</a></span> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b2">tl</font>] &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b3">tr</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">nt</font> <a href="trees_4.html#K6" title="TREES_4:func.6">-tree</a> (<font color="Olive" title="b2">tl</font>,<font color="Olive" title="b3">tr</font>)]
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="bintree1.html#T9" target="_self" onmouseover="rs('bintree1/T9')" onmouseout="rh()">Th9</a></span>;<br/>
<span class="kw">thus </span><a NAME="E3:24_1_1"/>
 for <font color="Olive" title="b1">x</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="Maroon" title="c1">G</font> holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">x</font>]
 <span class="kw">from</span> <span class="lab"><a class="ref" href="bintree1.html#S2" target="_self" onmouseover="rs('bintree1/S2')" onmouseout="rh()">BINTREE1:sch 2</a>(<a class="txt" href="#E1:24_1_1"><span class="lab"><font color="Green" title="E8">A1</font></span></a>, <a class="txt" href="#E2:24_1_1"><span class="lab"><font color="Green" title="E9">A2</font></span></a>);</span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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