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<b>deffunc </b><font color="Maroon">H<sub>12</sub></font>(  <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">G</font>) <b>-&gt; </b>   <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G</font> <a href="finseq_2.html#K3">*</a>  = <font color="Maroon">s2s</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">a<sub>1</sub></font>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>13</sub></font>(  <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">G</font>,   <a href="hidden.html#M1">set</a> ,   <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G</font> <a href="finseq_2.html#K3">*</a> ) <b>-&gt; </b>   <a href="finseq_2.html#M2">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G</font> <a href="finseq_2.html#K3">*</a>  = <span class="p1">(<span class="default"><font color="Maroon">s2s</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">a<sub>1</sub></font></span>)</span> <a href="lang1.html#K1">^</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15" target="_self">FlattenSeq</a> <font color="Maroon">a<sub>3</sub></font></span>)</span>;<br/>
<b>consider </b><font color="Maroon">f</font> being   <a href="funct_2.html#NM1">Function</a> of  <a href="dtconstr.html#K4" target="_self">TS</a> <font color="Maroon">G</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G</font> <a href="finseq_2.html#K3">*</a> <b> such that </b><br/><a NAME="E2:55_4_1"/><i><font color="Green">E84</font></i>: 
( ( for <font color="Olive">t</font> being  <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">G</font>  st <font color="Olive">t</font> <a href="hidden.html#R2">in</a>  <a href="lang1.html#K5">Terminals</a> <font color="Maroon">G</font> holds <br/><font color="Maroon">f</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="Olive">t</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>12</sub></font>(<font color="Olive">t</font>) ) &amp; ( for <font color="Olive">nt</font> being  <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">G</font><br/> for <font color="Olive">ts</font> being   <a href="trees_4.html#M1">FinSequence</a> of  <a href="dtconstr.html#K4" target="_self">TS</a> <font color="Maroon">G</font>  st <font color="Olive">nt</font> <a href="lang1.html#R1">==&gt;</a>  <a href="dtconstr.html#K1" target="_self">roots</a> <font color="Olive">ts</font> holds <br/><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Olive">nt</font> <a href="trees_4.html#K12">-tree</a> <font color="Olive">ts</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>13</sub></font>(<font color="Olive">nt</font>, <a href="dtconstr.html#K1" target="_self">roots</a> <font color="Olive">ts</font>,<font color="Maroon">f</font> <a href="finseqop.html#K5">*</a> <font color="Olive">ts</font>) ) )
 <b>from </b><i><a class="ref" href="dtconstr.html#S8" target="_self">DTCONSTR:sch 8</a>();<br/></i>
<a NAME="E3:55_4_1"/>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">tsg</font> is    <a href="finseq_2.html#M2">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G</font> <a href="finseq_2.html#K3">*</a> 
 
<b>by </b><i><a class="ref" href="dtconstr.html#T3" target="_self">Th3</a>, <a class="ref" href="funct_2.html#T7">FUNCT_2:7</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">IT</font> = <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">tsg</font> as    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G</font> ;<br/>
<b>take </b>
<font color="Maroon">IT</font>
;<br/>

<b>take </b>
<font color="Maroon">f</font>
;<br/>

<b>thus </b><a NAME="E5:55_4_1"/>
<font color="Maroon">IT</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">tsg</font>
 ;<br/>

<div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">t</font> be   <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">G</font>;<br/><b>assume </b><a NAME="E1:55_4_1_1"/>
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a>  <a href="lang1.html#K5">Terminals</a> <font color="Maroon">G</font>
 ;<br/><a NAME="E2:55_4_1_1"/><b>then </b>
<font color="Maroon">f</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">t</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">s2s</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">t</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E3:55_4_1_1"/>
<font color="Maroon">f</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">t</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">t</font></span><a href="lang1.html#K3">*&gt;</a></span>
 <b>by </b><i/>;<br/></div>
<b>end;</b></div>

<b>let </b><font color="Maroon">nt</font> be   <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">ts</font> be    <a href="trees_4.html#M1">FinSequence</a> of  <a href="dtconstr.html#K4" target="_self">TS</a> <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">rts</font> be   <a href="finseq_1.html#NM1">FinSequence</a>;<br/>





<b>assume </b><a NAME="E7:55_4_1"/><i><font color="Green">E85</font></i>: 
( <font color="Maroon">rts</font> <a href="hidden.html#R1">=</a>  <a href="dtconstr.html#K1" target="_self">roots</a> <font color="Maroon">ts</font> &amp; <font color="Maroon">nt</font> <a href="lang1.html#R1">==&gt;</a> <font color="Maroon">rts</font> )
 ;<br/>

<b>let </b><font color="Maroon">x</font> be    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G</font> <a href="finseq_2.html#K3">*</a> ;<br/>

<b>assume </b><a NAME="E8:55_4_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="finseqop.html#K5">*</a> <font color="Maroon">ts</font>
 ;<br/>

<b>hence </b><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">nt</font> <a href="trees_4.html#K12">-tree</a> <font color="Maroon">ts</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">s2s</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">nt</font></span>)</span> <a href="lang1.html#K1">^</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15" target="_self">FlattenSeq</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">nt</font></span><a href="lang1.html#K3">*&gt;</a></span> <a href="lang1.html#K1">^</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15" target="_self">FlattenSeq</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i/>
;<br/><br/>


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