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<b>deffunc </b><font color="Maroon">H<sub>3</sub></font>(   <a href="hidden.html#M1">set</a> ,   <a href="hidden.html#M1">set</a> ) <b>-&gt; </b>   <a href="hidden.html#M1">set</a>  = <font color="Maroon">a<sub>2</sub></font> <a href="xboole_0.html#K2">\/</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3"><a href="domain_1.html#K1">[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Maroon">H<sub>2</sub></font>(<font color="Olive">b<sub>1</sub></font>, <a href="mcart_1.html#K15">pr1</a> <span class="p1">(<span class="default"><a href="trees_3.html#K16">roots</a> <font color="Olive">b<sub>2</sub></font></span>)</span>, <a href="mcart_1.html#K16">pr2</a> <span class="p1">(<span class="default"><a href="trees_3.html#K16">roots</a> <font color="Olive">b<sub>2</sub></font></span>)</span>)</span><a href="domain_1.html#K1">]</a></span> <a href="trees_4.html#K4">-tree</a> <font color="Olive">b<sub>2</sub></font></span>)</span> where B is   <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">c<sub>1</sub></font>, B is    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">a<sub>2</sub></font> <a href="finseq_2.html#K3">*</a>  : ex <font color="Olive">b<sub>1</sub></font> being   <a href="finseq_1.html#M2">FinSequence</a> of  <a href="trees_3.html#K5">FinTrees</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,<a href="numbers.html#K5">NAT</a> </span><a href="zfmisc_1.html#K2">:]</a></span> st <br/>( <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>3</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="lang1.html#R1">==&gt;</a>  <a href="dtconstr.html#K2" target="_self">pr1</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K1" target="_self">roots</a> <font color="Olive">b<sub>3</sub></font></span>)</span> ) </span>}</span> ;<br/>
<b>consider </b><font color="Maroon">c<sub>2</sub></font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E2:21_1_1"/><i><font color="Green">E8</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="numbers.html#K5">NAT</a> 
 <b>and </b><br/><a NAME="E3:21_1_1"/><i><font color="Green">E9</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> 0 <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="trees_4.html#K2">root-tree</a> <span class="p3"><a href="domain_1.html#K1">[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font></span><a href="domain_1.html#K1">]</a></span></span>)</span> where B is   <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">c<sub>1</sub></font>, B is   <a href="nat_1.html#NM1">Nat</a> : ( ( <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>1</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">b<sub>1</sub></font>) ) or ( <font color="Olive">b<sub>1</sub></font> <a href="lang1.html#R1">==&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Olive">b<sub>1</sub></font>, <a href="xboole_0.html#K1">{}</a> , <a href="xboole_0.html#K1">{}</a> ) ) ) </span>}</span> 
 <b>and </b><br/><a NAME="E4:21_1_1"/><i><font color="Green">E10</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <font color="Maroon">c<sub>2</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="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>)
 <b>from </b><i><a class="ref" href="recdef_1.html#S3">RECDEF_1:sch 3</a>();<br/></i>
<a NAME="E5:21_1_1"/><i><font color="Green">E11</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <font color="Maroon">c<sub>2</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="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3"><a href="domain_1.html#K1">[</a><span class="default"><font color="Olive">b<sub>2</sub></font>,<font color="Maroon">H<sub>2</sub></font>(<font color="Olive">b<sub>2</sub></font>, <a href="mcart_1.html#K15">pr1</a> <span class="p1">(<span class="default"><a href="trees_3.html#K16">roots</a> <font color="Olive">b<sub>3</sub></font></span>)</span>, <a href="mcart_1.html#K16">pr2</a> <span class="p1">(<span class="default"><a href="trees_3.html#K16">roots</a> <font color="Olive">b<sub>3</sub></font></span>)</span>)</span><a href="domain_1.html#K1">]</a></span> <a href="trees_4.html#K4">-tree</a> <font color="Olive">b<sub>3</sub></font></span>)</span> where B is   <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">c<sub>1</sub></font>, B is    <a href="finseq_2.html#M2">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="finseq_2.html#K3">*</a>  : ex <font color="Olive">b<sub>1</sub></font> being   <a href="finseq_1.html#M2">FinSequence</a> of  <a href="trees_3.html#K5">FinTrees</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,<a href="numbers.html#K5">NAT</a> </span><a href="zfmisc_1.html#K2">:]</a></span> st <br/>( <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>4</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="lang1.html#R1">==&gt;</a>  <a href="dtconstr.html#K2" target="_self">pr1</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K1" target="_self">roots</a> <font color="Olive">b<sub>4</sub></font></span>)</span> ) </span>}</span> 
 
<b>by </b><i><a class="txt" href="dtconstr.html#E4:21_1_1"><i><font color="Green">E10</font></i></a></i>;<br/>
<a NAME="E6:21_1_1"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="trees_3.html#K5">FinTrees</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="trees_3.html#K10">`1</a> </span>)</span> where B is    <a href="trees_3.html#M5">Element</a> of  <a href="trees_3.html#K5">FinTrees</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,<a href="numbers.html#K5">NAT</a> </span><a href="zfmisc_1.html#K2">:]</a></span> : <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="card_3.html#K3">Union</a> <font color="Maroon">c<sub>2</sub></font> </span>}</span>  &amp; ( for <font color="Olive">b<sub>2</sub></font> being  <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="lang1.html#K5">Terminals</a> <font color="Maroon">c<sub>1</sub></font> holds <br/> <a href="trees_4.html#K2">root-tree</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> ) &amp; ( for <font color="Olive">b<sub>2</sub></font> being  <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">c<sub>1</sub></font><br/>for <font color="Olive">b<sub>3</sub></font> being   <a href="trees_4.html#M1">FinSequence</a> of <font color="Olive">b<sub>1</sub></font> st <font color="Olive">b<sub>2</sub></font> <a href="lang1.html#R1">==&gt;</a>  <a href="dtconstr.html#K1" target="_self">roots</a> <font color="Olive">b<sub>3</sub></font> holds <br/><font color="Olive">b<sub>2</sub></font> <a href="trees_4.html#K12">-tree</a> <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> ) &amp; ( for <font color="Olive">b<sub>2</sub></font> being  <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="trees_3.html#K5">FinTrees</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> st ( for <font color="Olive">b<sub>3</sub></font> being  <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="lang1.html#K5">Terminals</a> <font color="Maroon">c<sub>1</sub></font> holds <br/> <a href="trees_4.html#K2">root-tree</a> <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>2</sub></font> ) &amp; ( for <font color="Olive">b<sub>3</sub></font> being  <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">c<sub>1</sub></font><br/>for <font color="Olive">b<sub>4</sub></font> being   <a href="trees_4.html#M1">FinSequence</a> of <font color="Olive">b<sub>2</sub></font> st <font color="Olive">b<sub>3</sub></font> <a href="lang1.html#R1">==&gt;</a>  <a href="dtconstr.html#K1" target="_self">roots</a> <font color="Olive">b<sub>4</sub></font> holds <br/><font color="Olive">b<sub>3</sub></font> <a href="trees_4.html#K12">-tree</a> <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>2</sub></font> ) holds <br/><font color="Olive">b<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>2</sub></font> ) )
 
<b>from </b><i><a class="ref" href="dtconstr.html#S4" target="_self">DTCONSTR:sch 4</a>(<a class="txt" href="dtconstr.html#E2:21_1_1"><i><font color="Green">E8</font></i></a>, <a class="txt" href="dtconstr.html#E3:21_1_1"><i><font color="Green">E9</font></i></a>, <a class="txt" href="dtconstr.html#E5:21_1_1"><i><font color="Green">E11</font></i></a>);<br/></i>
<b>hence </b><a NAME="E7:21_1_1"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="trees_3.html#K5">FinTrees</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> st <br/>( ( for <font color="Olive">b<sub>2</sub></font> being  <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="lang1.html#K5">Terminals</a> <font color="Maroon">c<sub>1</sub></font> holds <br/> <a href="trees_4.html#K2">root-tree</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> ) &amp; ( for <font color="Olive">b<sub>2</sub></font> being  <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">c<sub>1</sub></font><br/>for <font color="Olive">b<sub>3</sub></font> being   <a href="trees_4.html#M1">FinSequence</a> of <font color="Olive">b<sub>1</sub></font> st <font color="Olive">b<sub>2</sub></font> <a href="lang1.html#R1">==&gt;</a>  <a href="dtconstr.html#K1" target="_self">roots</a> <font color="Olive">b<sub>3</sub></font> holds <br/><font color="Olive">b<sub>2</sub></font> <a href="trees_4.html#K12">-tree</a> <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> ) &amp; ( for <font color="Olive">b<sub>2</sub></font> being  <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="trees_3.html#K5">FinTrees</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> st ( for <font color="Olive">b<sub>3</sub></font> being  <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="lang1.html#K5">Terminals</a> <font color="Maroon">c<sub>1</sub></font> holds <br/> <a href="trees_4.html#K2">root-tree</a> <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>2</sub></font> ) &amp; ( for <font color="Olive">b<sub>3</sub></font> being  <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">c<sub>1</sub></font><br/>for <font color="Olive">b<sub>4</sub></font> being   <a href="trees_4.html#M1">FinSequence</a> of <font color="Olive">b<sub>2</sub></font> st <font color="Olive">b<sub>3</sub></font> <a href="lang1.html#R1">==&gt;</a>  <a href="dtconstr.html#K1" target="_self">roots</a> <font color="Olive">b<sub>4</sub></font> holds <br/><font color="Olive">b<sub>3</sub></font> <a href="trees_4.html#K12">-tree</a> <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>2</sub></font> ) holds <br/><font color="Olive">b<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>2</sub></font> ) )
 ;<br/>


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