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<b>set </b><font color="Maroon">c<sub>1</sub></font> = <font color="Maroon">F<sub>1</sub></font>();<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1">set</a> ] means <font color="Maroon">F<sub>5</sub></font>() <a href="funct_1.html#K1">.</a> <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>6</sub></font>() <a href="funct_1.html#K1">.</a> <font color="Maroon">a<sub>1</sub></font>;<br/>
<div><i><font color="Green">E11</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">F<sub>1</sub></font>();<br/><b>assume </b><a NAME="E1:24_1_1"/><i><font color="Green">E12</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="lang1.html#K5">Terminals</a> <font color="Maroon">F<sub>1</sub></font>()
 ;<br/><b>then </b><font color="Maroon">F<sub>5</sub></font>() <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="trees_4.html#K2">root-tree</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> = 
<font color="Maroon">F<sub>3</sub></font>(<font color="Maroon">c<sub>2</sub></font>)
<b>by </b><i><a class="txt" href="dtconstr.html#E1:24"><i><font color="Green">E9</font></i></a></i>
<br/>.= 
<font color="Maroon">F<sub>6</sub></font>() <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="trees_4.html#K2">root-tree</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="dtconstr.html#E2:24"><i><font color="Green">E10</font></i></a>, <a class="txt" href="dtconstr.html#E1:24_1_1"><i><font color="Green">E12</font></i></a></i>
;<br/><b>hence </b><a NAME="E3:24_1_1"/>
<font color="Maroon">S<sub>1</sub></font>[ <a href="trees_4.html#K2">root-tree</a> <font color="Maroon">c<sub>2</sub></font>]
 ;<br/></div><b>end;</b></div>
<div><i><font color="Green">E12</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">F<sub>1</sub></font>();<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="trees_4.html#M1">FinSequence</a> of  <a href="dtconstr.html#K4" target="_self">TS</a> <font color="Maroon">F<sub>1</sub></font>();<br/><b>assume </b><a NAME="E1:24_1_2"/><i><font color="Green">E13</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="lang1.html#R1">==&gt;</a>  <a href="dtconstr.html#K1" target="_self">roots</a> <font color="Maroon">c<sub>3</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="trees_2.html#NM6">DecoratedTree</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">F<sub>1</sub></font>() st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>3</sub></font> holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>] ) )
 ;<br/><a NAME="E2:24_1_2"/><i><font color="Green">E14</font></i>: 
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a>  <a href="dtconstr.html#K4" target="_self">TS</a> <font color="Maroon">F<sub>1</sub></font>()
 <b>by </b><i><a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/><a NAME="E3:24_1_2"/><b>then </b>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">F<sub>5</sub></font>()
 <b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/><a NAME="E4:24_1_2"/><b>then </b><i><font color="Green">E15</font></i>: 
(  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><font color="Maroon">F<sub>5</sub></font>() <a href="finseqop.html#K5">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">c<sub>3</sub></font> &amp;  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> )
 <b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a>, <a class="ref" href="relat_1.html#T46">RELAT_1:46</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">F<sub>5</sub></font>() <a href="finseqop.html#K5">*</a> <font color="Maroon">c<sub>3</sub></font> as   <a href="finseq_1.html#NM1">FinSequence</a> ;<br/><b>reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>4</sub></font> as    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">F<sub>2</sub></font>() ;<br/><a NAME="E7:24_1_2"/>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">F<sub>6</sub></font>()
 <b>by </b><i><a class="txt" href="dtconstr.html#E2:24_1_2"><i><font color="Green">E14</font></i></a>, <a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/><a NAME="E8:24_1_2"/><b>then </b><i><font color="Green">E16</font></i>: 
 <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><font color="Maroon">F<sub>6</sub></font>() <a href="finseqop.html#K5">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="relat_1.html#T46">RELAT_1:46</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>6</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:24_1_2_1"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><b>then reconsider </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font> as    <a href="trees_3.html#M5">Element</a> of  <a href="trees_3.html#K5">FinTrees</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">F<sub>1</sub></font>() <b>by </b><i><a class="ref" href="dtconstr.html#T2" target="_self">Th2</a></i>;<br/><a NAME="E3:24_1_2_1"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="dtconstr.html#E1:24_1_2_1"><i><font color="Green">E17</font></i></a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/><a NAME="E4:24_1_2_1"/><b>then </b><i><font color="Green">E18</font></i>: 
<font color="Maroon">F<sub>5</sub></font>() <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>6</sub></font>() <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="dtconstr.html#E1:24_1_2"><i><font color="Green">E13</font></i></a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon">F<sub>5</sub></font>() <a href="finseqop.html#K5">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font> = 
<font color="Maroon">F<sub>5</sub></font>() <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="dtconstr.html#E4:24_1_2"><i><font color="Green">E15</font></i></a>, <a class="txt" href="dtconstr.html#E1:24_1_2_1"><i><font color="Green">E17</font></i></a>, <a class="ref" href="funct_1.html#T22">FUNCT_1:22</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">F<sub>6</sub></font>() <a href="finseqop.html#K5">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="txt" href="dtconstr.html#E8:24_1_2"><i><font color="Green">E16</font></i></a>, <a class="txt" href="dtconstr.html#E1:24_1_2_1"><i><font color="Green">E17</font></i></a>, <a class="txt" href="dtconstr.html#E4:24_1_2_1"><i><font color="Green">E18</font></i></a>, <a class="ref" href="funct_1.html#T22">FUNCT_1:22</a></i>
;<br/></div><b>end;</b></div><a NAME="E10:24_1_2"/><b>then </b><i><font color="Green">E17</font></i>: 
<font color="Maroon">F<sub>5</sub></font>() <a href="finseqop.html#K5">*</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>6</sub></font>() <a href="finseqop.html#K5">*</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="dtconstr.html#E4:24_1_2"><i><font color="Green">E15</font></i></a>, <a class="txt" href="dtconstr.html#E8:24_1_2"><i><font color="Green">E16</font></i></a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><font color="Maroon">F<sub>5</sub></font>() <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="trees_4.html#K12">-tree</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> = 
<font color="Maroon">F<sub>4</sub></font>(<font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="dtconstr.html#K1" target="_self">roots</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>)
<b>by </b><i><a class="txt" href="dtconstr.html#E1:24"><i><font color="Green">E9</font></i></a>, <a class="txt" href="dtconstr.html#E1:24_1_2"><i><font color="Green">E13</font></i></a></i>
<br/>.= 
<font color="Maroon">F<sub>6</sub></font>() <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="trees_4.html#K12">-tree</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="dtconstr.html#E2:24"><i><font color="Green">E10</font></i></a>, <a class="txt" href="dtconstr.html#E1:24_1_2"><i><font color="Green">E13</font></i></a>, <a class="txt" href="dtconstr.html#E10:24_1_2"><i><font color="Green">E17</font></i></a></i>
;<br/><b>hence </b><a NAME="E12:24_1_2"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">c<sub>2</sub></font> <a href="trees_4.html#K12">-tree</a> <font color="Maroon">c<sub>3</sub></font>]
 ;<br/></div><b>end;</b></div>
<a NAME="E3:24_1"/><i><font color="Green">E13</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="trees_2.html#NM6">DecoratedTree</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">F<sub>1</sub></font>() st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="dtconstr.html#K4" target="_self">TS</a> <font color="Maroon">F<sub>1</sub></font>() holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>]
 
<b>from </b><i><a class="ref" href="dtconstr.html#S7" target="_self">DTCONSTR:sch 7</a>(<a class="txt" href="dtconstr.html#E1:24_1"><i><font color="Green">E11</font></i></a>, <a class="txt" href="dtconstr.html#E2:24_1"><i><font color="Green">E12</font></i></a>);<br/></i>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:24_1_3"/><i><font color="Green">E14</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="dtconstr.html#K4" target="_self">TS</a> <font color="Maroon">F<sub>1</sub></font>()
 ;<br/><b>then reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>2</sub></font> as    <a href="trees_3.html#M5">Element</a> of  <a href="trees_3.html#K5">FinTrees</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">F<sub>1</sub></font>() ;<br/><a NAME="E3:24_1_3"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><b>hence </b><a NAME="E4:24_1_3"/>
<font color="Maroon">F<sub>5</sub></font>() <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>6</sub></font>() <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="dtconstr.html#E3:24_1"><i><font color="Green">E13</font></i></a>, <a class="txt" href="dtconstr.html#E1:24_1_3"><i><font color="Green">E14</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:24_1"/>
<font color="Maroon">F<sub>5</sub></font>() <a href="funct_2.html#R2">=</a> <font color="Maroon">F<sub>6</sub></font>()
 <b>by </b><i><a class="ref" href="funct_2.html#T18">FUNCT_2:18</a></i>;<br/>


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