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<b>let </b><font color="Maroon">c<sub>12</sub></font>, <font color="Maroon">c<sub>13</sub></font> be    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>8</sub></font>;<br/>

<b>given </b><font color="Maroon">c<sub>14</sub></font> being   <a href="funct_2.html#NM1">Function</a> of  <a href="dtconstr.html#K4" target="_self">TS</a> <font color="Maroon">c<sub>8</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>8</sub></font> <a href="finseq_2.html#K3">*</a> <b> such that </b><a NAME="E1:55_5_2"/><i><font color="Green">E42</font></i>: 
( <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>14</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">c<sub>8</sub></font> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="lang1.html#K5">Terminals</a> <font color="Maroon">c<sub>8</sub></font> holds <br/><font color="Maroon">c<sub>14</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="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Olive">b<sub>1</sub></font></span><a href="lang1.html#K3">*&gt;</a></span> ) &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">c<sub>8</sub></font><br/>for <font color="Olive">b<sub>2</sub></font> being   <a href="trees_4.html#M1">FinSequence</a> of  <a href="dtconstr.html#K4" target="_self">TS</a> <font color="Maroon">c<sub>8</sub></font><br/>for <font color="Olive">b<sub>3</sub></font> being  <a href="finseq_1.html#NM1">FinSequence</a> st <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="dtconstr.html#K1" target="_self">roots</a> <font color="Olive">b<sub>2</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="lang1.html#R1">==&gt;</a> <font color="Olive">b<sub>3</sub></font> holds <br/>for <font color="Olive">b<sub>4</sub></font> being   <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>8</sub></font> <a href="finseq_2.html#K3">*</a>  st <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>14</sub></font> <a href="finseqop.html#K5">*</a> <font color="Olive">b<sub>2</sub></font> holds <br/><font color="Maroon">c<sub>14</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="trees_4.html#K12">-tree</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15" target="_self">FlattenSeq</a> <font color="Olive">b<sub>4</sub></font></span>)</span> <a href="lang1.html#K1">^</a> <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Olive">b<sub>1</sub></font></span><a href="lang1.html#K3">*&gt;</a></span> ) )
 ;<br/>

<b>given </b><font color="Maroon">c<sub>15</sub></font> being   <a href="funct_2.html#NM1">Function</a> of  <a href="dtconstr.html#K4" target="_self">TS</a> <font color="Maroon">c<sub>8</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>8</sub></font> <a href="finseq_2.html#K3">*</a> <b> such that </b><a NAME="E2:55_5_2"/><i><font color="Green">E43</font></i>: 
( <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>15</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">c<sub>8</sub></font> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="lang1.html#K5">Terminals</a> <font color="Maroon">c<sub>8</sub></font> holds <br/><font color="Maroon">c<sub>15</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="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Olive">b<sub>1</sub></font></span><a href="lang1.html#K3">*&gt;</a></span> ) &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">c<sub>8</sub></font><br/>for <font color="Olive">b<sub>2</sub></font> being   <a href="trees_4.html#M1">FinSequence</a> of  <a href="dtconstr.html#K4" target="_self">TS</a> <font color="Maroon">c<sub>8</sub></font><br/>for <font color="Olive">b<sub>3</sub></font> being  <a href="finseq_1.html#NM1">FinSequence</a> st <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="dtconstr.html#K1" target="_self">roots</a> <font color="Olive">b<sub>2</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="lang1.html#R1">==&gt;</a> <font color="Olive">b<sub>3</sub></font> holds <br/>for <font color="Olive">b<sub>4</sub></font> being   <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>8</sub></font> <a href="finseq_2.html#K3">*</a>  st <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>15</sub></font> <a href="finseqop.html#K5">*</a> <font color="Olive">b<sub>2</sub></font> holds <br/><font color="Maroon">c<sub>15</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="trees_4.html#K12">-tree</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15" target="_self">FlattenSeq</a> <font color="Olive">b<sub>4</sub></font></span>)</span> <a href="lang1.html#K1">^</a> <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Olive">b<sub>1</sub></font></span><a href="lang1.html#K3">*&gt;</a></span> ) )
 ;<br/>

<div><i><font color="Green">E44</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="55_5_2_1"><b>now </b></a><div class="add"><div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">c<sub>16</sub></font> be   <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">c<sub>8</sub></font>;<br/><b>assume </b><a NAME="E1:55_5_2_1_1"/>
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R2">in</a>  <a href="lang1.html#K5">Terminals</a> <font color="Maroon">c<sub>8</sub></font>
 ;<br/><b>hence </b><font color="Maroon">c<sub>14</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>16</sub></font></span>)</span> = 
<span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>16</sub></font></span><a href="lang1.html#K3">*&gt;</a></span>
<b>by </b><i><a class="txt" href="dtconstr.html#E1:55_5_2"><i><font color="Green">E42</font></i></a></i>
<br/>.= 
<font color="Maroon">H<sub>12</sub></font>(<font color="Maroon">c<sub>16</sub></font>)
<b>by </b><i><a class="txt" href="dtconstr.html#E7:55"><i><font color="Green">E41</font></i></a></i>
;<br/><br/></div>
<b>end;</b></div><b>let </b><font color="Maroon">c<sub>16</sub></font> be   <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">c<sub>8</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>17</sub></font> be    <a href="trees_4.html#M1">FinSequence</a> of  <a href="dtconstr.html#K4" target="_self">TS</a> <font color="Maroon">c<sub>8</sub></font>;<br/><b>assume </b><a NAME="E2:55_5_2_1"/>
<font color="Maroon">c<sub>16</sub></font> <a href="lang1.html#R1">==&gt;</a>  <a href="dtconstr.html#K1" target="_self">roots</a> <font color="Maroon">c<sub>17</sub></font>
 ;<br/><b>hence </b><font color="Maroon">c<sub>14</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="trees_4.html#K12">-tree</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="dtconstr.html#K15" target="_self">FlattenSeq</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="finseqop.html#K5">*</a> <font color="Maroon">c<sub>17</sub></font></span>)</span></span>)</span> <a href="lang1.html#K1">^</a> <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>16</sub></font></span><a href="lang1.html#K3">*&gt;</a></span>
<b>by </b><i><a class="txt" href="dtconstr.html#E1:55_5_2"><i><font color="Green">E42</font></i></a></i>
<br/>.= 
<font color="Maroon">H<sub>13</sub></font>(<font color="Maroon">c<sub>16</sub></font>, <a href="dtconstr.html#K1" target="_self">roots</a> <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="finseqop.html#K5">*</a> <font color="Maroon">c<sub>17</sub></font>)
<b>by </b><i><a class="txt" href="dtconstr.html#E7:55"><i><font color="Green">E41</font></i></a></i>
;<br/><br/></div><b>end;</b></div>
<div><i><font color="Green">E45</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="55_5_2_2"><b>now </b></a><div class="add"><div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">c<sub>16</sub></font> be   <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">c<sub>8</sub></font>;<br/><b>assume </b><a NAME="E1:55_5_2_2_1"/>
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R2">in</a>  <a href="lang1.html#K5">Terminals</a> <font color="Maroon">c<sub>8</sub></font>
 ;<br/><b>hence </b><font color="Maroon">c<sub>15</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>16</sub></font></span>)</span> = 
<span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>16</sub></font></span><a href="lang1.html#K3">*&gt;</a></span>
<b>by </b><i><a class="txt" href="dtconstr.html#E2:55_5_2"><i><font color="Green">E43</font></i></a></i>
<br/>.= 
<font color="Maroon">H<sub>12</sub></font>(<font color="Maroon">c<sub>16</sub></font>)
<b>by </b><i><a class="txt" href="dtconstr.html#E7:55"><i><font color="Green">E41</font></i></a></i>
;<br/><br/></div>
<b>end;</b></div><b>let </b><font color="Maroon">c<sub>16</sub></font> be   <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">c<sub>8</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>17</sub></font> be    <a href="trees_4.html#M1">FinSequence</a> of  <a href="dtconstr.html#K4" target="_self">TS</a> <font color="Maroon">c<sub>8</sub></font>;<br/><b>assume </b><a NAME="E2:55_5_2_2"/>
<font color="Maroon">c<sub>16</sub></font> <a href="lang1.html#R1">==&gt;</a>  <a href="dtconstr.html#K1" target="_self">roots</a> <font color="Maroon">c<sub>17</sub></font>
 ;<br/><b>hence </b><font color="Maroon">c<sub>15</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="trees_4.html#K12">-tree</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="dtconstr.html#K15" target="_self">FlattenSeq</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="finseqop.html#K5">*</a> <font color="Maroon">c<sub>17</sub></font></span>)</span></span>)</span> <a href="lang1.html#K1">^</a> <span class="p1"><a href="lang1.html#K3">&lt;*</a><span class="default"><font color="Maroon">c<sub>16</sub></font></span><a href="lang1.html#K3">*&gt;</a></span>
<b>by </b><i><a class="txt" href="dtconstr.html#E2:55_5_2"><i><font color="Green">E43</font></i></a></i>
<br/>.= 
<font color="Maroon">H<sub>13</sub></font>(<font color="Maroon">c<sub>16</sub></font>, <a href="dtconstr.html#K1" target="_self">roots</a> <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="finseqop.html#K5">*</a> <font color="Maroon">c<sub>17</sub></font>)
<b>by </b><i><a class="txt" href="dtconstr.html#E7:55"><i><font color="Green">E41</font></i></a></i>
;<br/><br/></div><b>end;</b></div>
<a NAME="E5:55_5_2"/>
<font color="Maroon">c<sub>14</sub></font> <a href="funct_2.html#R2">=</a> <font color="Maroon">c<sub>15</sub></font>
 
<b>from </b><i><a class="ref" href="dtconstr.html#S9" target="_self">DTCONSTR:sch 9</a>(<a class="txt" href="dtconstr.html#E3:55_5_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="dtconstr.html#E4:55_5_2"><i><font color="Green">E45</font></i></a>);<br/></i>
<b>hence </b><a NAME="E6:55_5_2"/>
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="txt" href="dtconstr.html#E1:55_5_2"><i><font color="Green">E42</font></i></a>, <a class="txt" href="dtconstr.html#E2:55_5_2"><i><font color="Green">E43</font></i></a></i>;<br/>


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