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<span class="kw">let </span><font color="Maroon" title="c1">G</font> be   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> ; <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">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="Maroon" title="c1">G</font><br/>  for <font color="Olive" title="b2">nt</font> being   <a href="lang1.html#NM1" title="LANG1:NM.1">Symbol</a> of <font color="Maroon" title="c1">G</font>  st <font color="Olive" title="b2">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="b1">ts</font> holds <br/>( <font color="Olive" title="b2">nt</font> is   <a href="dtconstr.html#NM3" title="DTCONSTR:NM.3">NonTerminal</a> of <font color="Maroon" title="c1">G</font> &amp;  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Olive" title="b1">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="b1">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="b1">ts</font> &amp;  ex <font color="Olive" title="b3">tl</font>, <font color="Olive" title="b4">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 <br/>(  <a href="dtconstr.html#K1" title="DTCONSTR:func.1">roots</a> <font color="Olive" title="b1">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="b3">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="b4">tr</font></span>)</span></span><a href="pre_poly.html#K4" title="PRE_POLY:func.4">*&gt;</a></span> &amp; <font color="Olive" title="b3">tl</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">ts</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 &amp; <font color="Olive" title="b4">tr</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">ts</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 &amp; <font color="Olive" title="b2">nt</font> <a href="trees_4.html#K8" title="TREES_4:func.8">-tree</a> <font color="Olive" title="b1">ts</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">nt</font> <a href="trees_4.html#K6" title="TREES_4:func.6">-tree</a> (<font color="Olive" title="b3">tl</font>,<font color="Olive" title="b4">tr</font>) &amp; <font color="Olive" title="b3">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="b1">ts</font> &amp; <font color="Olive" title="b4">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="b1">ts</font> ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">ts</font> be    <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="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">  for <font color="Olive" title="b1">nt</font> being   <a href="lang1.html#NM1" title="LANG1:NM.1">Symbol</a> of <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>  <a href="dtconstr.html#K1" title="DTCONSTR:func.1">roots</a> <font color="Maroon" title="c2">ts</font> holds <br/>( <font color="Olive" title="b1">nt</font> is   <a href="dtconstr.html#NM3" title="DTCONSTR:NM.3">NonTerminal</a> of <font color="Maroon" title="c1">G</font> &amp;  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">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="Maroon" title="c2">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="Maroon" title="c2">ts</font> &amp;  ex <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 <br/>(  <a href="dtconstr.html#K1" title="DTCONSTR:func.1">roots</a> <font color="Maroon" title="c2">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="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="Olive" title="b2">tl</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">ts</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 &amp; <font color="Olive" title="b3">tr</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">ts</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 &amp; <font color="Olive" title="b1">nt</font> <a href="trees_4.html#K8" title="TREES_4:func.8">-tree</a> <font color="Maroon" title="c2">ts</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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>) &amp; <font color="Olive" title="b2">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="Maroon" title="c2">ts</font> &amp; <font color="Olive" title="b3">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="Maroon" title="c2">ts</font> ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">nt</font> be   <a href="lang1.html#NM1" title="LANG1:NM.1">Symbol</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" title="c3">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="Maroon" title="c2">ts</font> implies ( <font color="Maroon" title="c3">nt</font> is   <a href="dtconstr.html#NM3" title="DTCONSTR:NM.3">NonTerminal</a> of <font color="Maroon" title="c1">G</font> &amp;  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">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="Maroon" title="c2">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="Maroon" title="c2">ts</font> &amp;  ex <font color="Olive" title="b1">tl</font>, <font color="Olive" title="b2">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 <br/>(  <a href="dtconstr.html#K1" title="DTCONSTR:func.1">roots</a> <font color="Maroon" title="c2">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="b1">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="b2">tr</font></span>)</span></span><a href="pre_poly.html#K4" title="PRE_POLY:func.4">*&gt;</a></span> &amp; <font color="Olive" title="b1">tl</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">ts</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 &amp; <font color="Olive" title="b2">tr</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">ts</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 &amp; <font color="Maroon" title="c3">nt</font> <a href="trees_4.html#K8" title="TREES_4:func.8">-tree</a> <font color="Maroon" title="c2">ts</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">nt</font> <a href="trees_4.html#K6" title="TREES_4:func.6">-tree</a> (<font color="Olive" title="b1">tl</font>,<font color="Olive" title="b2">tr</font>) &amp; <font color="Olive" title="b1">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="Maroon" title="c2">ts</font> &amp; <font color="Olive" title="b2">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="Maroon" title="c2">ts</font> ) ) )</span><br/>





<span class="kw">assume </span><a NAME="E1:18"/><span class="lab"><font color="Green" title="E8">A1</font></span>: 
<font color="Maroon" title="c3">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="Maroon" title="c2">ts</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" title="c3">nt</font> is   <a href="dtconstr.html#NM3" title="DTCONSTR:NM.3">NonTerminal</a> of <font color="Maroon" title="c1">G</font> &amp;  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">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="Maroon" title="c2">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="Maroon" title="c2">ts</font> &amp;  ex <font color="Olive" title="b1">tl</font>, <font color="Olive" title="b2">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 <br/>(  <a href="dtconstr.html#K1" title="DTCONSTR:func.1">roots</a> <font color="Maroon" title="c2">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="b1">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="b2">tr</font></span>)</span></span><a href="pre_poly.html#K4" title="PRE_POLY:func.4">*&gt;</a></span> &amp; <font color="Olive" title="b1">tl</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">ts</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 &amp; <font color="Olive" title="b2">tr</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">ts</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 &amp; <font color="Maroon" title="c3">nt</font> <a href="trees_4.html#K8" title="TREES_4:func.8">-tree</a> <font color="Maroon" title="c2">ts</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">nt</font> <a href="trees_4.html#K6" title="TREES_4:func.6">-tree</a> (<font color="Olive" title="b1">tl</font>,<font color="Olive" title="b2">tr</font>) &amp; <font color="Olive" title="b1">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="Maroon" title="c2">ts</font> &amp; <font color="Olive" title="b2">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="Maroon" title="c2">ts</font> ) )</span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">rtl</font>, <font color="Maroon" title="c5">rtr</font> being   <a href="lang1.html#NM1" title="LANG1:NM.1">Symbol</a> of <font color="Maroon" title="c1">G</font><span class="kw"> such that </span><br/><a NAME="E3:18"/><span class="lab"><font color="Green" title="E9">A2</font></span>: 
 <a href="dtconstr.html#K1" title="DTCONSTR:func.1">roots</a> <font color="Maroon" title="c2">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"><font color="Maroon" title="c4">rtl</font>,<font color="Maroon" title="c5">rtr</font></span><a href="pre_poly.html#K4" title="PRE_POLY:func.4">*&gt;</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="bintree1.html#D4" target="_self" onmouseover="rs('bintree1/D4')" onmouseout="rh()">Def4</a></span>;<br/>
<a NAME="E4:18"/>
<font color="Maroon" title="c3">nt</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">s</font> where <font color="Olive" title="b1">s</font> is   <a href="lang1.html#NM1" title="LANG1:NM.1">Symbol</a> of <font color="Maroon" title="c1">G</font> :  ex <font color="Olive" title="b2">rts</font> being   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a> st <font color="Olive" title="b1">s</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a> <font color="Olive" title="b2">rts</font> </span> } </span> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:18"><span class="lab"><font color="Green" title="E8">A1</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:18"/>
<font color="Maroon" title="c3">nt</font> is   <a href="dtconstr.html#NM3" title="DTCONSTR:NM.3">NonTerminal</a> of <font color="Maroon" title="c1">G</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="lang1.html#D3" onmouseover="rs('lang1/D3')" onmouseout="rh()">LANG1:def 3</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"> (  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">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="Maroon" title="c2">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="Maroon" title="c2">ts</font> &amp;  ex <font color="Olive" title="b1">tl</font>, <font color="Olive" title="b2">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 <br/>(  <a href="dtconstr.html#K1" title="DTCONSTR:func.1">roots</a> <font color="Maroon" title="c2">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="b1">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="b2">tr</font></span>)</span></span><a href="pre_poly.html#K4" title="PRE_POLY:func.4">*&gt;</a></span> &amp; <font color="Olive" title="b1">tl</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">ts</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 &amp; <font color="Olive" title="b2">tr</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">ts</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 &amp; <font color="Maroon" title="c3">nt</font> <a href="trees_4.html#K8" title="TREES_4:func.8">-tree</a> <font color="Maroon" title="c2">ts</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">nt</font> <a href="trees_4.html#K6" title="TREES_4:func.6">-tree</a> (<font color="Olive" title="b1">tl</font>,<font color="Olive" title="b2">tr</font>) &amp; <font color="Olive" title="b1">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="Maroon" title="c2">ts</font> &amp; <font color="Olive" title="b2">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="Maroon" title="c2">ts</font> ) )</span><br/>

<a NAME="E6:18"/><span class="lab"><font color="Green" title="E10">A3</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1"><a href="pre_poly.html#K4" title="PRE_POLY:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c4">rtl</font>,<font color="Maroon" title="c5">rtr</font></span><a href="pre_poly.html#K4" title="PRE_POLY:func.4">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T44" onmouseover="rs('finseq_1/T44')" onmouseout="rh()">FINSEQ_1:44</a></span>;<br/>
<a NAME="E7:18"/><span class="lab"><font color="Green" title="E11">A4</font></span>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="pre_poly.html#K4" title="PRE_POLY:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c4">rtl</font>,<font color="Maroon" title="c5">rtr</font></span><a href="pre_poly.html#K4" title="PRE_POLY:func.4">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">ts</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:18"><span class="lab"><font color="Green" title="E9">A2</font></span></a>, <a class="ref" href="trees_3.html#D18" onmouseover="rs('trees_3/D18')" onmouseout="rh()">TREES_3:def 18</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:18"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:18"><span class="lab"><font color="Green" title="E10">A3</font></span></a>, <a class="ref" href="finseq_1.html#T2" onmouseover="rs('finseq_1/T2')" onmouseout="rh()">FINSEQ_1:2</a>, <a class="ref" href="finseq_1.html#D3" onmouseover="rs('finseq_1/D3')" onmouseout="rh()">FINSEQ_1:def 3</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"> ( 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="Maroon" title="c2">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="Maroon" title="c2">ts</font> &amp;  ex <font color="Olive" title="b1">tl</font>, <font color="Olive" title="b2">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 <br/>(  <a href="dtconstr.html#K1" title="DTCONSTR:func.1">roots</a> <font color="Maroon" title="c2">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="b1">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="b2">tr</font></span>)</span></span><a href="pre_poly.html#K4" title="PRE_POLY:func.4">*&gt;</a></span> &amp; <font color="Olive" title="b1">tl</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">ts</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 &amp; <font color="Olive" title="b2">tr</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">ts</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 &amp; <font color="Maroon" title="c3">nt</font> <a href="trees_4.html#K8" title="TREES_4:func.8">-tree</a> <font color="Maroon" title="c2">ts</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">nt</font> <a href="trees_4.html#K6" title="TREES_4:func.6">-tree</a> (<font color="Olive" title="b1">tl</font>,<font color="Olive" title="b2">tr</font>) &amp; <font color="Olive" title="b1">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="Maroon" title="c2">ts</font> &amp; <font color="Olive" title="b2">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="Maroon" title="c2">ts</font> ) )</span><br/>

<span class="kw">hence </span><a NAME="E9:18"/><span class="lab"><font color="Green" title="E12">A5</font></span>: 
( 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="Maroon" title="c2">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="Maroon" title="c2">ts</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D2" onmouseover="rs('tarski/D2')" onmouseout="rh()">TARSKI:def 2</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">  ex <font color="Olive" title="b1">tl</font>, <font color="Olive" title="b2">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 <br/>(  <a href="dtconstr.html#K1" title="DTCONSTR:func.1">roots</a> <font color="Maroon" title="c2">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="b1">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="b2">tr</font></span>)</span></span><a href="pre_poly.html#K4" title="PRE_POLY:func.4">*&gt;</a></span> &amp; <font color="Olive" title="b1">tl</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">ts</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 &amp; <font color="Olive" title="b2">tr</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">ts</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 &amp; <font color="Maroon" title="c3">nt</font> <a href="trees_4.html#K8" title="TREES_4:func.8">-tree</a> <font color="Maroon" title="c2">ts</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">nt</font> <a href="trees_4.html#K6" title="TREES_4:func.6">-tree</a> (<font color="Olive" title="b1">tl</font>,<font color="Olive" title="b2">tr</font>) &amp; <font color="Olive" title="b1">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="Maroon" title="c2">ts</font> &amp; <font color="Olive" title="b2">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="Maroon" title="c2">ts</font> )</span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">tl</font> being   <a href="trees_2.html#NM4" title="TREES_2:NM.4">DecoratedTree</a><span class="kw"> such that </span><br/><a NAME="E11:18"/><span class="lab"><font color="Green" title="E13">A6</font></span>: 
<font color="Maroon" title="c6">tl</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">ts</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
 <span class="kw">and </span><br/><a NAME="E12:18"/><span class="lab"><font color="Green" title="E14">A7</font></span>: 
<span class="p1"><a href="pre_poly.html#K4" title="PRE_POLY:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c4">rtl</font>,<font color="Maroon" title="c5">rtr</font></span><a href="pre_poly.html#K4" title="PRE_POLY:func.4">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">tl</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:18"><span class="lab"><font color="Green" title="E9">A2</font></span></a>, <a class="ref" href="trees_3.html#D18" onmouseover="rs('trees_3/D18')" onmouseout="rh()">TREES_3:def 18</a></span>;<br/>
<a NAME="E13:18"/><span class="lab"><font color="Green" title="E15">A8</font></span>: 
(  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c2">ts</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="dtconstr.html#K4" title="DTCONSTR:func.4">TS</a> <font color="Maroon" title="c1">G</font> &amp; <font color="Maroon" title="c6">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="Maroon" title="c2">ts</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:18"><span class="lab"><font color="Green" title="E12">A5</font></span></a>, <a class="txt" href="#E11:18"><span class="lab"><font color="Green" title="E13">A6</font></span></a>, <a class="ref" href="finseq_1.html#D4" onmouseover="rs('finseq_1/D4')" onmouseout="rh()">FINSEQ_1:def 4</a>, <a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c7">tr</font> being   <a href="trees_2.html#NM4" title="TREES_2:NM.4">DecoratedTree</a><span class="kw"> such that </span><br/><a NAME="E15:18"/><span class="lab"><font color="Green" title="E16">A9</font></span>: 
<font color="Maroon" title="c7">tr</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">ts</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2
 <span class="kw">and </span><br/><a NAME="E16:18"/><span class="lab"><font color="Green" title="E17">A10</font></span>: 
<span class="p1"><a href="pre_poly.html#K4" title="PRE_POLY:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c4">rtl</font>,<font color="Maroon" title="c5">rtr</font></span><a href="pre_poly.html#K4" title="PRE_POLY:func.4">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">tr</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:18"><span class="lab"><font color="Green" title="E9">A2</font></span></a>, <a class="txt" href="#E9:18"><span class="lab"><font color="Green" title="E12">A5</font></span></a>, <a class="ref" href="trees_3.html#D18" onmouseover="rs('trees_3/D18')" onmouseout="rh()">TREES_3:def 18</a></span>;<br/>
<a NAME="E17:18"/>
<font color="Maroon" title="c7">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="Maroon" title="c2">ts</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:18"><span class="lab"><font color="Green" title="E12">A5</font></span></a>, <a class="txt" href="#E15:18"><span class="lab"><font color="Green" title="E16">A9</font></span></a>, <a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c8">tl</font> = <font color="Maroon" title="c6">tl</font>, <font color="Maroon" title="c9">tr</font> = <font color="Maroon" title="c7">tr</font> as    <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> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:18"><span class="lab"><font color="Green" title="E15">A8</font></span></a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c8">tl</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">  ex <font color="Olive" title="b1">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 <br/>(  <a href="dtconstr.html#K1" title="DTCONSTR:func.1">roots</a> <font color="Maroon" title="c2">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="Maroon" title="c8">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="b1">tr</font></span>)</span></span><a href="pre_poly.html#K4" title="PRE_POLY:func.4">*&gt;</a></span> &amp; <font color="Maroon" title="c8">tl</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">ts</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 &amp; <font color="Olive" title="b1">tr</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">ts</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 &amp; <font color="Maroon" title="c3">nt</font> <a href="trees_4.html#K8" title="TREES_4:func.8">-tree</a> <font color="Maroon" title="c2">ts</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">nt</font> <a href="trees_4.html#K6" title="TREES_4:func.6">-tree</a> (<font color="Maroon" title="c8">tl</font>,<font color="Olive" title="b1">tr</font>) &amp; <font color="Maroon" title="c8">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="Maroon" title="c2">ts</font> &amp; <font color="Olive" title="b1">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="Maroon" title="c2">ts</font> )</span><br/>

<span class="kw">take </span>
<font color="Maroon" title="c9">tr</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"> (  <a href="dtconstr.html#K1" title="DTCONSTR:func.1">roots</a> <font color="Maroon" title="c2">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="Maroon" title="c8">tl</font></span>)</span>,<span class="p2">(<span class="default"><a href="bintree1.html#K1" title="BINTREE1:func.1">root-label</a> <font color="Maroon" title="c9">tr</font></span>)</span></span><a href="pre_poly.html#K4" title="PRE_POLY:func.4">*&gt;</a></span> &amp; <font color="Maroon" title="c8">tl</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">ts</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 &amp; <font color="Maroon" title="c9">tr</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">ts</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 &amp; <font color="Maroon" title="c3">nt</font> <a href="trees_4.html#K8" title="TREES_4:func.8">-tree</a> <font color="Maroon" title="c2">ts</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">nt</font> <a href="trees_4.html#K6" title="TREES_4:func.6">-tree</a> (<font color="Maroon" title="c8">tl</font>,<font color="Maroon" title="c9">tr</font>) &amp; <font color="Maroon" title="c8">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="Maroon" title="c2">ts</font> &amp; <font color="Maroon" title="c9">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="Maroon" title="c2">ts</font> )</span><br/>

<span class="kw">thus </span><a NAME="E19:18"/>
 <a href="dtconstr.html#K1" title="DTCONSTR:func.1">roots</a> <font color="Maroon" title="c2">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="Maroon" title="c8">tl</font></span>)</span>,<span class="p2">(<span class="default"><a href="bintree1.html#K1" title="BINTREE1:func.1">root-label</a> <font color="Maroon" title="c9">tr</font></span>)</span></span><a href="pre_poly.html#K4" title="PRE_POLY:func.4">*&gt;</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:18"><span class="lab"><font color="Green" title="E9">A2</font></span></a>, <a class="txt" href="#E12:18"><span class="lab"><font color="Green" title="E14">A7</font></span></a>, <a class="txt" href="#E16:18"><span class="lab"><font color="Green" title="E17">A10</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"> ( <font color="Maroon" title="c8">tl</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">ts</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 &amp; <font color="Maroon" title="c9">tr</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">ts</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 &amp; <font color="Maroon" title="c3">nt</font> <a href="trees_4.html#K8" title="TREES_4:func.8">-tree</a> <font color="Maroon" title="c2">ts</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">nt</font> <a href="trees_4.html#K6" title="TREES_4:func.6">-tree</a> (<font color="Maroon" title="c8">tl</font>,<font color="Maroon" title="c9">tr</font>) &amp; <font color="Maroon" title="c8">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="Maroon" title="c2">ts</font> &amp; <font color="Maroon" title="c9">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="Maroon" title="c2">ts</font> )</span><br/>

 <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2"><a href="pre_poly.html#K4" title="PRE_POLY:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c4">rtl</font>,<font color="Maroon" title="c5">rtr</font></span><a href="pre_poly.html#K4" title="PRE_POLY:func.4">*&gt;</a></span></span>)</span> = 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="pre_poly.html#K4" title="PRE_POLY:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c4">rtl</font>,<font color="Maroon" title="c5">rtr</font></span><a href="pre_poly.html#K4" title="PRE_POLY:func.4">*&gt;</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D3" onmouseover="rs('finseq_1/D3')" onmouseout="rh()">FINSEQ_1:def 3</a></span>
<br/>.= 
 <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">ts</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:18"><span class="lab"><font color="Green" title="E11">A4</font></span></a>, <a class="ref" href="finseq_1.html#D3" onmouseover="rs('finseq_1/D3')" onmouseout="rh()">FINSEQ_1:def 3</a></span>
;<br/>
<a NAME="E21:18"/><span class="kw">then </span>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">ts</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:18"><span class="lab"><font color="Green" title="E10">A3</font></span></a>, <a class="ref" href="finseq_1.html#T6" onmouseover="rs('finseq_1/T6')" onmouseout="rh()">FINSEQ_1:6</a></span>;<br/>
<a NAME="E22:18"/><span class="kw">then </span>
<font color="Maroon" title="c2">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"><font color="Maroon" title="c8">tl</font>,<font color="Maroon" title="c9">tr</font></span><a href="pre_poly.html#K4" title="PRE_POLY:func.4">*&gt;</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:18"><span class="lab"><font color="Green" title="E13">A6</font></span></a>, <a class="txt" href="#E15:18"><span class="lab"><font color="Green" title="E16">A9</font></span></a>, <a class="ref" href="finseq_1.html#T44" onmouseover="rs('finseq_1/T44')" onmouseout="rh()">FINSEQ_1:44</a></span>;<br/>
<span class="kw">hence </span><a NAME="E23:18"/>
( <font color="Maroon" title="c8">tl</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">ts</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 &amp; <font color="Maroon" title="c9">tr</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">ts</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 &amp; <font color="Maroon" title="c3">nt</font> <a href="trees_4.html#K8" title="TREES_4:func.8">-tree</a> <font color="Maroon" title="c2">ts</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">nt</font> <a href="trees_4.html#K6" title="TREES_4:func.6">-tree</a> (<font color="Maroon" title="c8">tl</font>,<font color="Maroon" title="c9">tr</font>) )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="trees_4.html#D6" onmouseover="rs('trees_4/D6')" onmouseout="rh()">TREES_4:def 6</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"> ( <font color="Maroon" title="c8">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="Maroon" title="c2">ts</font> &amp; <font color="Maroon" title="c9">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="Maroon" title="c2">ts</font> )</span><br/>

<span class="kw">thus </span><a NAME="E24:18"/>
( <font color="Maroon" title="c8">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="Maroon" title="c2">ts</font> &amp; <font color="Maroon" title="c9">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="Maroon" title="c2">ts</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:18"><span class="lab"><font color="Green" title="E12">A5</font></span></a>, <a class="txt" href="#E11:18"><span class="lab"><font color="Green" title="E13">A6</font></span></a>, <a class="txt" href="#E15:18"><span class="lab"><font color="Green" title="E16">A9</font></span></a>, <a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</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>
