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<b>let </b><font color="Maroon" title="c9">it1</font>, <font color="Maroon" title="c10">it2</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  ex <font color="Olive" title="b1">f</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="dtconstr.html#K4" title="DTCONSTR:func.4">TS</a> <a href="scm_comp.html#K1" title="SCM_COMP:func.1">SCM-AE</a> , <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ,<span class="p1">(<span class="default">the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> </span>)</span> st <br/>( <font color="Maroon" title="c9">it1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">term</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">aux</font> &amp; ( for <font color="Olive" title="b2">t</font> being  <a href="dtconstr.html#NM2" title="DTCONSTR:NM.2">Terminal</a> of <a href="scm_comp.html#K1" title="SCM_COMP:func.1">SCM-AE</a>   ex <font color="Olive" title="b3">g</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ,the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  st <br/>( <font color="Olive" title="b3">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="scm_comp.html#K3" title="SCM_COMP:func.3">root-tree</a> <font color="Olive" title="b2">t</font></span>)</span> &amp; ( for <font color="Olive" title="b4">n</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  holds  <font color="Olive" title="b3">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <font color="Olive" title="b4">n</font></span>)</span> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <span class="p3">(<span class="default"><a href="scm_comp.html#K4" title="SCM_COMP:func.4">@</a> <font color="Olive" title="b2">t</font></span>)</span></span>)</span></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span> ) ) ) &amp; ( for <font color="Olive" title="b2">nt</font> being  <a href="dtconstr.html#NM3" title="DTCONSTR:NM.3">NonTerminal</a> of <a href="scm_comp.html#K1" title="SCM_COMP:func.1">SCM-AE</a> <br/> for <font color="Olive" title="b3">t1</font>, <font color="Olive" title="b4">t2</font> being  <a href="scm_comp.html#NM1" title="SCM_COMP:NM.1">bin-term</a><br/> for <font color="Olive" title="b5">rtl</font>, <font color="Olive" title="b6">rtr</font> being  <a href="lang1.html#NM1" title="LANG1:NM.1">Symbol</a> of <a href="scm_comp.html#K1" title="SCM_COMP:func.1">SCM-AE</a>   st <font color="Olive" title="b5">rtl</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bintree1.html#K1" title="BINTREE1:func.1">root-label</a> <font color="Olive" title="b3">t1</font> &amp; <font color="Olive" title="b6">rtr</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bintree1.html#K1" title="BINTREE1:func.1">root-label</a> <font color="Olive" title="b4">t2</font> &amp; <font color="Olive" title="b2">nt</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a> <span class="p1"><a href="lang1.html#K4" title="LANG1:func.4">&lt;*</a><span class="default"><font color="Olive" title="b5">rtl</font>,<font color="Olive" title="b6">rtr</font></span><a href="lang1.html#K4" title="LANG1:func.4">*&gt;</a></span> holds <br/> ex <font color="Olive" title="b7">g</font>, <font color="Olive" title="b8">f1</font>, <font color="Olive" title="b9">f2</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ,the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  st <br/>( <font color="Olive" title="b7">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">nt</font> <a href="scm_comp.html#K2" title="SCM_COMP:func.2">-tree</a> <font color="Olive" title="b3">t1</font>,<font color="Olive" title="b4">t2</font></span>)</span> &amp; <font color="Olive" title="b8">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">t1</font> &amp; <font color="Olive" title="b9">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">t2</font> &amp; ( for <font color="Olive" title="b10">n</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  holds  <font color="Olive" title="b7">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b10">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b8">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b10">n</font></span>)</span> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <span class="p2">(<span class="default"><font color="Olive" title="b9">f2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Olive" title="b10">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <span class="p1">(<span class="default"><a href="scm_comp.html#K14" title="SCM_COMP:func.14">Selfwork</a> <font color="Olive" title="b2">nt</font>,<font color="Olive" title="b10">n</font></span>)</span> ) ) ) ) &amp;  ex <font color="Olive" title="b1">f</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="dtconstr.html#K4" title="DTCONSTR:func.4">TS</a> <a href="scm_comp.html#K1" title="SCM_COMP:func.1">SCM-AE</a> , <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ,<span class="p1">(<span class="default">the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> </span>)</span> st <br/>( <font color="Maroon" title="c10">it2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">term</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">aux</font> &amp; ( for <font color="Olive" title="b2">t</font> being  <a href="dtconstr.html#NM2" title="DTCONSTR:NM.2">Terminal</a> of <a href="scm_comp.html#K1" title="SCM_COMP:func.1">SCM-AE</a>   ex <font color="Olive" title="b3">g</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ,the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  st <br/>( <font color="Olive" title="b3">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="scm_comp.html#K3" title="SCM_COMP:func.3">root-tree</a> <font color="Olive" title="b2">t</font></span>)</span> &amp; ( for <font color="Olive" title="b4">n</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  holds  <font color="Olive" title="b3">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <font color="Olive" title="b4">n</font></span>)</span> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <span class="p3">(<span class="default"><a href="scm_comp.html#K4" title="SCM_COMP:func.4">@</a> <font color="Olive" title="b2">t</font></span>)</span></span>)</span></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span> ) ) ) &amp; ( for <font color="Olive" title="b2">nt</font> being  <a href="dtconstr.html#NM3" title="DTCONSTR:NM.3">NonTerminal</a> of <a href="scm_comp.html#K1" title="SCM_COMP:func.1">SCM-AE</a> <br/> for <font color="Olive" title="b3">t1</font>, <font color="Olive" title="b4">t2</font> being  <a href="scm_comp.html#NM1" title="SCM_COMP:NM.1">bin-term</a><br/> for <font color="Olive" title="b5">rtl</font>, <font color="Olive" title="b6">rtr</font> being  <a href="lang1.html#NM1" title="LANG1:NM.1">Symbol</a> of <a href="scm_comp.html#K1" title="SCM_COMP:func.1">SCM-AE</a>   st <font color="Olive" title="b5">rtl</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bintree1.html#K1" title="BINTREE1:func.1">root-label</a> <font color="Olive" title="b3">t1</font> &amp; <font color="Olive" title="b6">rtr</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bintree1.html#K1" title="BINTREE1:func.1">root-label</a> <font color="Olive" title="b4">t2</font> &amp; <font color="Olive" title="b2">nt</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a> <span class="p1"><a href="lang1.html#K4" title="LANG1:func.4">&lt;*</a><span class="default"><font color="Olive" title="b5">rtl</font>,<font color="Olive" title="b6">rtr</font></span><a href="lang1.html#K4" title="LANG1:func.4">*&gt;</a></span> holds <br/> ex <font color="Olive" title="b7">g</font>, <font color="Olive" title="b8">f1</font>, <font color="Olive" title="b9">f2</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ,the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  st <br/>( <font color="Olive" title="b7">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">nt</font> <a href="scm_comp.html#K2" title="SCM_COMP:func.2">-tree</a> <font color="Olive" title="b3">t1</font>,<font color="Olive" title="b4">t2</font></span>)</span> &amp; <font color="Olive" title="b8">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">t1</font> &amp; <font color="Olive" title="b9">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">t2</font> &amp; ( for <font color="Olive" title="b10">n</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  holds  <font color="Olive" title="b7">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b10">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b8">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b10">n</font></span>)</span> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <span class="p2">(<span class="default"><font color="Olive" title="b9">f2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Olive" title="b10">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <span class="p1">(<span class="default"><a href="scm_comp.html#K14" title="SCM_COMP:func.14">Selfwork</a> <font color="Olive" title="b2">nt</font>,<font color="Olive" title="b10">n</font></span>)</span> ) ) ) ) implies <font color="Maroon" title="c9">it1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">it2</font> )</span><br/>

<b>given </b><font color="Maroon" title="c11">f1</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="dtconstr.html#K4" title="DTCONSTR:func.4">TS</a> <a href="scm_comp.html#K1" title="SCM_COMP:func.1">SCM-AE</a> , <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ,<span class="p1">(<span class="default">the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> </span>)</span><b> such that </b><a NAME="E2:20_1_2"/><i><font color="Green" title="E13">A2</font></i>: 
<font color="Maroon" title="c9">it1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">term</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">aux</font>
 <b>and </b><br/><a NAME="E3:20_1_2"/><i><font color="Green" title="E14">A3</font></i>: 
( ( for <font color="Olive" title="b1">t</font> being  <a href="dtconstr.html#NM2" title="DTCONSTR:NM.2">Terminal</a> of <a href="scm_comp.html#K1" title="SCM_COMP:func.1">SCM-AE</a>   ex <font color="Olive" title="b2">g</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ,the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  st <br/>( <font color="Olive" title="b2">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="scm_comp.html#K3" title="SCM_COMP:func.3">root-tree</a> <font color="Olive" title="b1">t</font></span>)</span> &amp; ( for <font color="Olive" title="b3">n</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  holds  <font color="Olive" title="b2">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">t</font>,<font color="Olive" title="b3">n</font>) ) ) ) &amp; ( for <font color="Olive" title="b1">nt</font> being  <a href="dtconstr.html#NM3" title="DTCONSTR:NM.3">NonTerminal</a> of <a href="scm_comp.html#K1" title="SCM_COMP:func.1">SCM-AE</a> <br/> for <font color="Olive" title="b2">t1</font>, <font color="Olive" title="b3">t2</font> being  <a href="scm_comp.html#NM1" title="SCM_COMP:NM.1">bin-term</a><br/> for <font color="Olive" title="b4">rtl</font>, <font color="Olive" title="b5">rtr</font> being  <a href="lang1.html#NM1" title="LANG1:NM.1">Symbol</a> of <a href="scm_comp.html#K1" title="SCM_COMP:func.1">SCM-AE</a>   st <font color="Olive" title="b4">rtl</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bintree1.html#K1" title="BINTREE1:func.1">root-label</a> <font color="Olive" title="b2">t1</font> &amp; <font color="Olive" title="b5">rtr</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bintree1.html#K1" title="BINTREE1:func.1">root-label</a> <font color="Olive" title="b3">t2</font> &amp; <font color="Olive" title="b1">nt</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a> <span class="p1"><a href="lang1.html#K4" title="LANG1:func.4">&lt;*</a><span class="default"><font color="Olive" title="b4">rtl</font>,<font color="Olive" title="b5">rtr</font></span><a href="lang1.html#K4" title="LANG1:func.4">*&gt;</a></span> holds <br/> ex <font color="Olive" title="b6">g</font>, <font color="Olive" title="b7">g1</font>, <font color="Olive" title="b8">g2</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ,the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  st <br/>( <font color="Olive" title="b6">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">nt</font> <a href="scm_comp.html#K2" title="SCM_COMP:func.2">-tree</a> <font color="Olive" title="b2">t1</font>,<font color="Olive" title="b3">t2</font></span>)</span> &amp; <font color="Olive" title="b7">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">t1</font> &amp; <font color="Olive" title="b8">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">t2</font> &amp; ( for <font color="Olive" title="b9">n</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  holds  <font color="Olive" title="b6">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b9">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Olive" title="b1">nt</font>,<font color="Olive" title="b7">g1</font>,<font color="Olive" title="b8">g2</font>,<font color="Olive" title="b9">n</font>) ) ) ) )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( for <font color="Olive" title="b1">f</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="dtconstr.html#K4" title="DTCONSTR:func.4">TS</a> <a href="scm_comp.html#K1" title="SCM_COMP:func.1">SCM-AE</a> , <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ,<span class="p1">(<span class="default">the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> </span>)</span>  holds <br/>(  not <font color="Maroon" title="c10">it2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">term</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">aux</font> or  ex <font color="Olive" title="b2">t</font> being  <a href="dtconstr.html#NM2" title="DTCONSTR:NM.2">Terminal</a> of <a href="scm_comp.html#K1" title="SCM_COMP:func.1">SCM-AE</a>  st <br/>for <font color="Olive" title="b3">g</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ,the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>   holds <br/>(  not <font color="Olive" title="b3">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="scm_comp.html#K3" title="SCM_COMP:func.3">root-tree</a> <font color="Olive" title="b2">t</font></span>)</span> or  ex <font color="Olive" title="b4">n</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  st not <font color="Olive" title="b3">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="lang1.html#K3" title="LANG1:func.3">&lt;*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <font color="Olive" title="b4">n</font></span>)</span> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <span class="p3">(<span class="default"><a href="scm_comp.html#K4" title="SCM_COMP:func.4">@</a> <font color="Olive" title="b2">t</font></span>)</span></span>)</span></span><a href="lang1.html#K3" title="LANG1:func.3">*&gt;</a></span> ) or  ex <font color="Olive" title="b2">nt</font> being  <a href="dtconstr.html#NM3" title="DTCONSTR:NM.3">NonTerminal</a> of <a href="scm_comp.html#K1" title="SCM_COMP:func.1">SCM-AE</a>  ex <font color="Olive" title="b3">t1</font>, <font color="Olive" title="b4">t2</font> being  <a href="scm_comp.html#NM1" title="SCM_COMP:NM.1">bin-term</a> ex <font color="Olive" title="b5">rtl</font>, <font color="Olive" title="b6">rtr</font> being  <a href="lang1.html#NM1" title="LANG1:NM.1">Symbol</a> of <a href="scm_comp.html#K1" title="SCM_COMP:func.1">SCM-AE</a>  st <br/>( <font color="Olive" title="b5">rtl</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bintree1.html#K1" title="BINTREE1:func.1">root-label</a> <font color="Olive" title="b3">t1</font> &amp; <font color="Olive" title="b6">rtr</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bintree1.html#K1" title="BINTREE1:func.1">root-label</a> <font color="Olive" title="b4">t2</font> &amp; <font color="Olive" title="b2">nt</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a> <span class="p1"><a href="lang1.html#K4" title="LANG1:func.4">&lt;*</a><span class="default"><font color="Olive" title="b5">rtl</font>,<font color="Olive" title="b6">rtr</font></span><a href="lang1.html#K4" title="LANG1:func.4">*&gt;</a></span> &amp; ( for <font color="Olive" title="b7">g</font>, <font color="Olive" title="b8">f1</font>, <font color="Olive" title="b9">f2</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ,the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>   holds <br/>(  not <font color="Olive" title="b7">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">nt</font> <a href="scm_comp.html#K2" title="SCM_COMP:func.2">-tree</a> <font color="Olive" title="b3">t1</font>,<font color="Olive" title="b4">t2</font></span>)</span> or  not <font color="Olive" title="b8">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">t1</font> or  not <font color="Olive" title="b9">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">t2</font> or  ex <font color="Olive" title="b10">n</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  st not <font color="Olive" title="b7">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b10">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b8">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b10">n</font></span>)</span> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <span class="p2">(<span class="default"><font color="Olive" title="b9">f2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Olive" title="b10">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <span class="p1">(<span class="default"><a href="scm_comp.html#K14" title="SCM_COMP:func.14">Selfwork</a> <font color="Olive" title="b2">nt</font>,<font color="Olive" title="b10">n</font></span>)</span> ) ) ) ) or <font color="Maroon" title="c9">it1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">it2</font> )</span><br/>

<b>given </b><font color="Maroon" title="c12">f2</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="dtconstr.html#K4" title="DTCONSTR:func.4">TS</a> <a href="scm_comp.html#K1" title="SCM_COMP:func.1">SCM-AE</a> , <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ,<span class="p1">(<span class="default">the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> </span>)</span><b> such that </b><a NAME="E5:20_1_2"/><i><font color="Green" title="E15">A4</font></i>: 
<font color="Maroon" title="c10">it2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">f2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">term</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">aux</font>
 <b>and </b><br/><a NAME="E6:20_1_2"/><i><font color="Green" title="E16">A5</font></i>: 
( ( for <font color="Olive" title="b1">t</font> being  <a href="dtconstr.html#NM2" title="DTCONSTR:NM.2">Terminal</a> of <a href="scm_comp.html#K1" title="SCM_COMP:func.1">SCM-AE</a>   ex <font color="Olive" title="b2">g</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ,the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  st <br/>( <font color="Olive" title="b2">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">f2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="scm_comp.html#K3" title="SCM_COMP:func.3">root-tree</a> <font color="Olive" title="b1">t</font></span>)</span> &amp; ( for <font color="Olive" title="b3">n</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  holds  <font color="Olive" title="b2">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">t</font>,<font color="Olive" title="b3">n</font>) ) ) ) &amp; ( for <font color="Olive" title="b1">nt</font> being  <a href="dtconstr.html#NM3" title="DTCONSTR:NM.3">NonTerminal</a> of <a href="scm_comp.html#K1" title="SCM_COMP:func.1">SCM-AE</a> <br/> for <font color="Olive" title="b2">t1</font>, <font color="Olive" title="b3">t2</font> being  <a href="scm_comp.html#NM1" title="SCM_COMP:NM.1">bin-term</a><br/> for <font color="Olive" title="b4">rtl</font>, <font color="Olive" title="b5">rtr</font> being  <a href="lang1.html#NM1" title="LANG1:NM.1">Symbol</a> of <a href="scm_comp.html#K1" title="SCM_COMP:func.1">SCM-AE</a>   st <font color="Olive" title="b4">rtl</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bintree1.html#K1" title="BINTREE1:func.1">root-label</a> <font color="Olive" title="b2">t1</font> &amp; <font color="Olive" title="b5">rtr</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bintree1.html#K1" title="BINTREE1:func.1">root-label</a> <font color="Olive" title="b3">t2</font> &amp; <font color="Olive" title="b1">nt</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a> <span class="p1"><a href="lang1.html#K4" title="LANG1:func.4">&lt;*</a><span class="default"><font color="Olive" title="b4">rtl</font>,<font color="Olive" title="b5">rtr</font></span><a href="lang1.html#K4" title="LANG1:func.4">*&gt;</a></span> holds <br/> ex <font color="Olive" title="b6">g</font>, <font color="Olive" title="b7">g1</font>, <font color="Olive" title="b8">g2</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ,the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  st <br/>( <font color="Olive" title="b6">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">f2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">nt</font> <a href="scm_comp.html#K2" title="SCM_COMP:func.2">-tree</a> <font color="Olive" title="b2">t1</font>,<font color="Olive" title="b3">t2</font></span>)</span> &amp; <font color="Olive" title="b7">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">f2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">t1</font> &amp; <font color="Olive" title="b8">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">f2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">t2</font> &amp; ( for <font color="Olive" title="b9">n</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  holds  <font color="Olive" title="b6">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b9">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Olive" title="b1">nt</font>,<font color="Olive" title="b7">g1</font>,<font color="Olive" title="b8">g2</font>,<font color="Olive" title="b9">n</font>) ) ) ) )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c9">it1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">it2</font></span><br/>

<a NAME="E7:20_1_2"/>
<font color="Maroon" title="c11">f1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c12">f2</font>
 
<b>from </b><i><a class="ref" href="bintree1.html#S6" title="BINTREE1:sch.6">BINTREE1:sch 6</a>(<a class="txt" href="scm_comp.html#E3:20_1_2"><i><font color="Green" title="E14">A3</font></i></a>, <a class="txt" href="scm_comp.html#E6:20_1_2"><i><font color="Green" title="E16">A5</font></i></a>);<br/></i>
<b>hence </b><a NAME="E8:20_1_2"/>
<font color="Maroon" title="c9">it1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">it2</font>
 <b>by </b><i><a class="txt" href="scm_comp.html#E2:20_1_2"><i><font color="Green" title="E13">A2</font></i></a>, <a class="txt" href="scm_comp.html#E5:20_1_2"><i><font color="Green" title="E15">A4</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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