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<b>let </b><font color="Maroon">it1</font> be    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="ami_1.html#U4">Instructions</a> of <a href="ami_3.html#K1">SCM</a> , <font color="Maroon">it2</font> be    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="ami_1.html#U4">Instructions</a> of <a href="ami_3.html#K1">SCM</a> ;<br/>

<b>given </b><font color="Maroon">f1</font> being   <a href="funct_2.html#NM1">Function</a> of  <a href="dtconstr.html#K4">TS</a> <a href="scm_comp.html#K1" target="_self">SCM-AE</a> , <a href="fraenkel.html#K1">Funcs</a> <a href="numbers.html#K5">NAT</a> ,<span class="p1">(<span class="default">the <a href="ami_1.html#U4">Instructions</a> of <a href="ami_3.html#K1">SCM</a>  <a href="finseq_2.html#K3">*</a> </span>)</span><b> such that </b><a NAME="E1:20_1_2"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">it1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">f1</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">term</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">aux</font>
 <b>and </b><br/><a NAME="E2:20_1_2"/><i><font color="Green">E36</font></i>: 
( ( for <font color="Olive">t</font> being  <a href="dtconstr.html#NM2">Terminal</a> of <a href="scm_comp.html#K1" target="_self">SCM-AE</a>   ex <font color="Olive">g</font> being  <a href="funct_2.html#NM1">Function</a> of  <a href="numbers.html#K5">NAT</a> ,the <a href="ami_1.html#U4">Instructions</a> of <a href="ami_3.html#K1">SCM</a>  <a href="finseq_2.html#K3">*</a>  st <br/>( <font color="Olive">g</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f1</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="scm_comp.html#K3" target="_self">root-tree</a> <font color="Olive">t</font></span>)</span> &amp; ( for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Olive">g</font> <a href="funct_2.html#K3">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">t</font>,<font color="Olive">n</font>) ) ) ) &amp; ( for <font color="Olive">nt</font> being  <a href="dtconstr.html#NM3">NonTerminal</a> of <a href="scm_comp.html#K1" target="_self">SCM-AE</a> <br/> for <font color="Olive">t1</font>, <font color="Olive">t2</font> being  <a href="scm_comp.html#NM1">bin-term</a><br/> for <font color="Olive">rtl</font>, <font color="Olive">rtr</font> being  <a href="lang1.html#NM1">Symbol</a> of <a href="scm_comp.html#K1" target="_self">SCM-AE</a>   st <font color="Olive">rtl</font> <a href="hidden.html#R1">=</a>  <a href="bintree1.html#K1">root-label</a> <font color="Olive">t1</font> &amp; <font color="Olive">rtr</font> <a href="hidden.html#R1">=</a>  <a href="bintree1.html#K1">root-label</a> <font color="Olive">t2</font> &amp; <font color="Olive">nt</font> <a href="lang1.html#R1">==&gt;</a> <span class="p1"><a href="lang1.html#K4">&lt;*</a><span class="default"><font color="Olive">rtl</font>,<font color="Olive">rtr</font></span><a href="lang1.html#K4">*&gt;</a></span> holds <br/> ex <font color="Olive">g</font>, <font color="Olive">g1</font>, <font color="Olive">g2</font> being  <a href="funct_2.html#NM1">Function</a> of  <a href="numbers.html#K5">NAT</a> ,the <a href="ami_1.html#U4">Instructions</a> of <a href="ami_3.html#K1">SCM</a>  <a href="finseq_2.html#K3">*</a>  st <br/>( <font color="Olive">g</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f1</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Olive">nt</font> <a href="scm_comp.html#K2" target="_self">-tree</a> <font color="Olive">t1</font>,<font color="Olive">t2</font></span>)</span> &amp; <font color="Olive">g1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f1</font> <a href="funct_2.html#K3">.</a> <font color="Olive">t1</font> &amp; <font color="Olive">g2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f1</font> <a href="funct_2.html#K3">.</a> <font color="Olive">t2</font> &amp; ( for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Olive">g</font> <a href="funct_2.html#K3">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Olive">nt</font>,<font color="Olive">g1</font>,<font color="Olive">g2</font>,<font color="Olive">n</font>) ) ) ) )
 ;<br/>

<b>given </b><font color="Maroon">f2</font> being   <a href="funct_2.html#NM1">Function</a> of  <a href="dtconstr.html#K4">TS</a> <a href="scm_comp.html#K1" target="_self">SCM-AE</a> , <a href="fraenkel.html#K1">Funcs</a> <a href="numbers.html#K5">NAT</a> ,<span class="p1">(<span class="default">the <a href="ami_1.html#U4">Instructions</a> of <a href="ami_3.html#K1">SCM</a>  <a href="finseq_2.html#K3">*</a> </span>)</span><b> such that </b><a NAME="E3:20_1_2"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">it2</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">term</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">aux</font>
 <b>and </b><br/><a NAME="E4:20_1_2"/><i><font color="Green">E39</font></i>: 
( ( for <font color="Olive">t</font> being  <a href="dtconstr.html#NM2">Terminal</a> of <a href="scm_comp.html#K1" target="_self">SCM-AE</a>   ex <font color="Olive">g</font> being  <a href="funct_2.html#NM1">Function</a> of  <a href="numbers.html#K5">NAT</a> ,the <a href="ami_1.html#U4">Instructions</a> of <a href="ami_3.html#K1">SCM</a>  <a href="finseq_2.html#K3">*</a>  st <br/>( <font color="Olive">g</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="scm_comp.html#K3" target="_self">root-tree</a> <font color="Olive">t</font></span>)</span> &amp; ( for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Olive">g</font> <a href="funct_2.html#K3">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">t</font>,<font color="Olive">n</font>) ) ) ) &amp; ( for <font color="Olive">nt</font> being  <a href="dtconstr.html#NM3">NonTerminal</a> of <a href="scm_comp.html#K1" target="_self">SCM-AE</a> <br/> for <font color="Olive">t1</font>, <font color="Olive">t2</font> being  <a href="scm_comp.html#NM1">bin-term</a><br/> for <font color="Olive">rtl</font>, <font color="Olive">rtr</font> being  <a href="lang1.html#NM1">Symbol</a> of <a href="scm_comp.html#K1" target="_self">SCM-AE</a>   st <font color="Olive">rtl</font> <a href="hidden.html#R1">=</a>  <a href="bintree1.html#K1">root-label</a> <font color="Olive">t1</font> &amp; <font color="Olive">rtr</font> <a href="hidden.html#R1">=</a>  <a href="bintree1.html#K1">root-label</a> <font color="Olive">t2</font> &amp; <font color="Olive">nt</font> <a href="lang1.html#R1">==&gt;</a> <span class="p1"><a href="lang1.html#K4">&lt;*</a><span class="default"><font color="Olive">rtl</font>,<font color="Olive">rtr</font></span><a href="lang1.html#K4">*&gt;</a></span> holds <br/> ex <font color="Olive">g</font>, <font color="Olive">g1</font>, <font color="Olive">g2</font> being  <a href="funct_2.html#NM1">Function</a> of  <a href="numbers.html#K5">NAT</a> ,the <a href="ami_1.html#U4">Instructions</a> of <a href="ami_3.html#K1">SCM</a>  <a href="finseq_2.html#K3">*</a>  st <br/>( <font color="Olive">g</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Olive">nt</font> <a href="scm_comp.html#K2" target="_self">-tree</a> <font color="Olive">t1</font>,<font color="Olive">t2</font></span>)</span> &amp; <font color="Olive">g1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> <a href="funct_2.html#K3">.</a> <font color="Olive">t1</font> &amp; <font color="Olive">g2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> <a href="funct_2.html#K3">.</a> <font color="Olive">t2</font> &amp; ( for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Olive">g</font> <a href="funct_2.html#K3">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Olive">nt</font>,<font color="Olive">g1</font>,<font color="Olive">g2</font>,<font color="Olive">n</font>) ) ) ) )
 ;<br/>

<a NAME="E5:20_1_2"/>
<font color="Maroon">f1</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">f2</font>
 
<b>from </b><i><a class="ref" href="bintree1.html#S6">BINTREE1:sch 6</a>(, );<br/></i>
<b>hence </b><a NAME="E6:20_1_2"/>
<font color="Maroon">it1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">it2</font>
 <b>by </b><i>, </i>;<br/>


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