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<div class="add">

<span class="kw">set </span><font color="Maroon" title="c5">T2</font> =  <a href="trees_a.html#K3" title="TREES_A:func.3">tree</a> <font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">T1</font>;<br/>
<a NAME="E1:24_1_1"/><span class="lab"><font color="Green" title="E18">A2</font></span>: 
 <a href="trees_a.html#K3" title="TREES_A:func.3">tree</a> <font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">T1</font> is <font color="Maroon" title="c1">D</font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c6">y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a>,<a class="ref" href="relat_1.html#D19" title="RELAT_1:def.19">RELAT_1:def 19</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c6">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <span class="p1">(<span class="default"><a href="trees_a.html#K3" title="TREES_A:func.3">tree</a> <font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">T1</font></span>)</span> or <font color="Maroon" title="c6">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">D</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:24_1_1_1"/><span class="lab"><font color="Green" title="E19">A3</font></span>: 
<font color="Maroon" title="c6">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="trees_a.html#K3" title="TREES_A:func.3">tree</a> <font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">T1</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c6">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">D</font></span><br/>

<span class="kw">consider </span><font color="Maroon" title="c7">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E3:24_1_1_1"/><span class="lab"><font color="Green" title="E20">A4</font></span>: 
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="trees_a.html#K3" title="TREES_A:func.3">tree</a> <font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">T1</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E4:24_1_1_1"/><span class="lab"><font color="Green" title="E21">A5</font></span>: 
<font color="Maroon" title="c6">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="trees_a.html#K3" title="TREES_A:func.3">tree</a> <font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">T1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:24_1_1_1"><span class="lab"><font color="Green" title="E19">A3</font></span></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></span>;<br/>
<a NAME="E5:24_1_1_1"/><span class="lab"><font color="Green" title="E22">A6</font></span>: 
<font color="Maroon" title="c7">x</font> is    <a href="trees_1.html#M1" title="TREES_1:mode.1">Element</a> of  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="trees_a.html#K3" title="TREES_A:func.3">tree</a> <font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">T1</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:24_1_1_1"><span class="lab"><font color="Green" title="E20">A4</font></span></a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c8">q</font> = <font color="Maroon" title="c7">x</font> as    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:24_1_1_1"><span class="lab"><font color="Green" title="E22">A6</font></span></a></span>;<br/>
<a NAME="E7:24_1_1_1"/><span class="lab"><font color="Green" title="E23">A7</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="trees_a.html#K3" title="TREES_A:func.3">tree</a> <font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">T1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="trees_a.html#K1" title="TREES_A:func.1">tree</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c2">T</font></span>)</span>,<font color="Maroon" title="c3">P</font>,<span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">T1</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:24"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="ref" href="trees_a.html#D2" target="_self" title="TREES_A:def.2">Def2</a></span>;<br/>
<a NAME="E8:24_1_1_1"/><span class="lab"><font color="Green" title="E24">A8</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="trees_a.html#K3" title="TREES_A:func.3">tree</a> <font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">T1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">t1</font> where <font color="Olive" title="b1">t1</font> is    <a href="trees_1.html#M1" title="TREES_1:mode.1">Element</a> of  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c2">T</font> : for <font color="Olive" title="b2">p</font> being   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Olive" title="b2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">P</font> holds <br/> not <font color="Olive" title="b2">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">is_a_prefix_of</a> <font color="Olive" title="b1">t1</font> </span>}</span>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b1">p</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Olive" title="b2">s</font></span>)</span> where <font color="Olive" title="b1">p</font> is    <a href="trees_1.html#M1" title="TREES_1:mode.1">Element</a> of  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c2">T</font>, <font color="Olive" title="b2">s</font> is    <a href="trees_1.html#M1" title="TREES_1:mode.1">Element</a> of  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">T1</font> : <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">P</font> </span>}</span> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:24"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="txt" href="#E7:24_1_1_1"><span class="lab"><font color="Green" title="E23">A7</font></span></a>, <a class="ref" href="trees_a.html#T7" target="_self" title="TREES_A:th.7">Th7</a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_1_1_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:24_1_1_1_1"/>
( <font color="Maroon" title="c8">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">t1</font> where <font color="Olive" title="b1">t1</font> is    <a href="trees_1.html#M1" title="TREES_1:mode.1">Element</a> of  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c2">T</font> : for <font color="Olive" title="b2">p</font> being   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Olive" title="b2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">P</font> holds <br/> not <font color="Olive" title="b2">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">is_a_prefix_of</a> <font color="Olive" title="b1">t1</font> </span>}</span>  or <font color="Maroon" title="c8">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b1">p</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Olive" title="b2">s</font></span>)</span> where <font color="Olive" title="b1">p</font> is    <a href="trees_1.html#M1" title="TREES_1:mode.1">Element</a> of  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c2">T</font>, <font color="Olive" title="b2">s</font> is    <a href="trees_1.html#M1" title="TREES_1:mode.1">Element</a> of  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">T1</font> : <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">P</font> </span>}</span>  )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:24_1_1_1"><span class="lab"><font color="Green" title="E20">A4</font></span></a>, <a class="txt" href="#E8:24_1_1_1"><span class="lab"><font color="Green" title="E24">A8</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_1_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:24_1_1_1_1_1"/><span class="lab"><font color="Green" title="E25">A9</font></span>: 
<font color="Maroon" title="c8">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">t1</font> where <font color="Olive" title="b1">t1</font> is    <a href="trees_1.html#M1" title="TREES_1:mode.1">Element</a> of  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c2">T</font> : for <font color="Olive" title="b2">p</font> being   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Olive" title="b2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">P</font> holds <br/> not <font color="Olive" title="b2">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">is_a_prefix_of</a> <font color="Olive" title="b1">t1</font> </span>}</span> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c6">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">D</font></span><br/><div class="add"><a NAME="E2:24_1_1_1_1_1"/><span class="lab"><font color="Green" title="E26">A10</font></span>: 
<span class="p1">(<span class="default"><a href="trees_a.html#K3" title="TREES_A:func.3">tree</a> <font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">T1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">T</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">q</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:24"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="txt" href="#E3:24_1_1_1"><span class="lab"><font color="Green" title="E20">A4</font></span></a>, <a class="txt" href="#E1:24_1_1_1_1_1"><span class="lab"><font color="Green" title="E25">A9</font></span></a>, <a class="ref" href="trees_a.html#T15" target="_self" title="TREES_A:th.15">Th15</a></span>;<br/><div><span class="lab"><font color="Green" title="E27">A11</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1_1_1_1_1_1"><span class="kw">now </span></a><div class="add"><a NAME="E1:24_1_1_1_1_1_1"/><span class="lab"><font color="Green" title="E28">A12</font></span>: 
 ex <font color="Olive" title="b1">t9</font> being   <a href="trees_1.html#M1" title="TREES_1:mode.1">Element</a> of  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c2">T</font> st <br/>( <font color="Maroon" title="c8">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">t9</font> &amp; ( for <font color="Olive" title="b2">p</font> being   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Olive" title="b2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">P</font> holds <br/> not <font color="Olive" title="b2">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">is_a_prefix_of</a> <font color="Olive" title="b1">t9</font> ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:24_1_1_1_1_1"><span class="lab"><font color="Green" title="E25">A9</font></span></a></span>;<br/><span class="kw">thus </span><a NAME="E2:24_1_1_1_1_1_1"/>
<font color="Maroon" title="c8">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:24_1_1_1_1_1_1"><span class="lab"><font color="Green" title="E28">A12</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><a NAME="E4:24_1_1_1_1_1"/><span class="lab"><font color="Green" title="E28">A13</font></span>: 
<font color="Maroon" title="c6">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:24_1_1_1"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="txt" href="#E2:24_1_1_1_1_1"><span class="lab"><font color="Green" title="E26">A10</font></span></a>, <a class="txt" href="#E3:24_1_1_1_1_1"><span class="lab"><font color="Green" title="E27">A11</font></span></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></span>;<br/><a NAME="E5:24_1_1_1_1_1"/><span class="lab"><font color="Green" title="E29">A14</font></span>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c2">T</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">D</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D19" title="RELAT_1:def.19">RELAT_1:def 19</a></span>;<br/><span class="kw">thus </span><a NAME="E6:24_1_1_1_1_1"/>
<font color="Maroon" title="c6">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">D</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:24_1_1_1_1_1"><span class="lab"><font color="Green" title="E28">A13</font></span></a>, <a class="txt" href="#E5:24_1_1_1_1_1"><span class="lab"><font color="Green" title="E29">A14</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_1_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:24_1_1_1_1_2"/><span class="lab"><font color="Green" title="E25">A15</font></span>: 
<font color="Maroon" title="c8">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b1">p</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Olive" title="b2">s</font></span>)</span> where <font color="Olive" title="b1">p</font> is    <a href="trees_1.html#M1" title="TREES_1:mode.1">Element</a> of  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c2">T</font>, <font color="Olive" title="b2">s</font> is    <a href="trees_1.html#M1" title="TREES_1:mode.1">Element</a> of  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">T1</font> : <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">P</font> </span>}</span> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c6">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">D</font></span><br/><div class="add"><a NAME="E2:24_1_1_1_1_2"/><span class="lab"><font color="Green" title="E26">A16</font></span>: 
 ex <font color="Olive" title="b1">p</font> being   <a href="trees_1.html#M1" title="TREES_1:mode.1">Element</a> of  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c2">T</font> ex <font color="Olive" title="b2">r</font> being   <a href="trees_1.html#M1" title="TREES_1:mode.1">Element</a> of  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">T1</font> st <br/>( <font color="Maroon" title="c8">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">p</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Olive" title="b2">r</font> &amp; <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">P</font> &amp; <span class="p1">(<span class="default"><a href="trees_a.html#K3" title="TREES_A:func.3">tree</a> <font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">T1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">T1</font> <a href="trees_2.html#K3" title="TREES_2:func.3">.</a> <font color="Olive" title="b2">r</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:24_1_1_1"><span class="lab"><font color="Green" title="E20">A4</font></span></a>, <a class="txt" href="#E1:24_1_1_1_1_2"><span class="lab"><font color="Green" title="E25">A15</font></span></a>, <a class="ref" href="trees_a.html#T17" target="_self" title="TREES_A:th.17">Th17</a></span>;<br/><span class="kw">thus </span><a NAME="E3:24_1_1_1_1_2"/>
<font color="Maroon" title="c6">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">D</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:24_1_1_1"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="txt" href="#E2:24_1_1_1_1_2"><span class="lab"><font color="Green" title="E26">A16</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div><span class="kw">end;</span></div>
<span class="kw">thus </span><a NAME="E2:24_1_1"/>
 <a href="trees_a.html#K3" title="TREES_A:func.3">tree</a> <font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">T1</font> is   <a href="trees_2.html#NM5" title="TREES_2:NM.5">DecoratedTree</a> of <font color="Maroon" title="c1">D</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:24_1_1"><span class="lab"><font color="Green" title="E18">A2</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
