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<b>let </b><font color="Maroon" title="c10">nt</font> be   <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/><b>let </b><font color="Maroon" title="c11">t1</font>, <font color="Maroon" title="c12">t2</font> be   <a href="scm_comp.html#NM1" title="SCM_COMP:NM.1">bin-term</a>;<br/><b>let </b><font color="Maroon" title="c13">n</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c14">rtl</font>, <font color="Maroon" title="c15">rtr</font> be   <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> ;<br/>







<b>assume </b><a NAME="E1:22"/>
( <font color="Maroon" title="c14">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="Maroon" title="c11">t1</font> &amp; <font color="Maroon" title="c15">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="Maroon" title="c12">t2</font> &amp; <font color="Maroon" title="c10">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="Maroon" title="c14">rtl</font>,<font color="Maroon" title="c15">rtr</font></span><a href="lang1.html#K4" title="LANG1:func.4">*&gt;</a></span> )
 ;<br/>

<b>then consider </b><font color="Maroon" title="c16">g</font>, <font color="Maroon" title="c17">f1</font>, <font color="Maroon" title="c18">f2</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,the <a href="ami_1.html#U4" title="AMI_1:sel.4">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> <b> such that </b><br/><a NAME="E3:22"/><i><font color="Green" title="E17">A1</font></i>: 
( <font color="Maroon" title="c16">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">nt</font> <a href="scm_comp.html#K2" title="SCM_COMP:func.2">-tree</a> <font color="Maroon" title="c11">t1</font>,<font color="Maroon" title="c12">t2</font></span>)</span> &amp; <font color="Maroon" title="c17">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">t1</font> &amp; <font color="Maroon" title="c18">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">t2</font> &amp; ( for <font color="Olive" title="b1">n</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <font color="Maroon" title="c16">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">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="Maroon" title="c17">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">n</font></span>)</span> <a href="lang1.html#K1" title="LANG1:func.1">^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c18">f2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Olive" title="b1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</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="Maroon" title="c10">nt</font>,<font color="Olive" title="b1">n</font></span>)</span> ) )
 <b>by </b><i><a class="txt" href="scm_comp.html#E27"><i><font color="Green" title="E14">Lm4</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c19">f1n</font> = <font color="Maroon" title="c17">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c13">n</font>, <font color="Maroon" title="c20">f2n</font> = <font color="Maroon" title="c18">f2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of the <a href="ami_1.html#U4" title="AMI_1:sel.4">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>  ;<br/>
<a NAME="E5:22"/>
(  <a href="scm_comp.html#K15" title="SCM_COMP:func.15">SCM-Compile</a> <font color="Maroon" title="c11">t1</font>,<font color="Maroon" title="c13">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">f1n</font> &amp;  <a href="scm_comp.html#K15" title="SCM_COMP:func.15">SCM-Compile</a> <font color="Maroon" title="c12">t2</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c13">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">f2n</font> )
 
<b>by </b><i><a class="txt" href="scm_comp.html#E3:22"><i><font color="Green" title="E17">A1</font></i></a>, <a class="ref" href="scm_comp.html#D11" target="_self" title="SCM_COMP:def.11">Def11</a>, <a class="txt" href="scm_comp.html#E27"><i><font color="Green" title="E14">Lm4</font></i></a></i>;<br/>
<a NAME="E6:22"/><b>then </b>
<font color="Maroon" title="c16">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c13">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scm_comp.html#K15" title="SCM_COMP:func.15">SCM-Compile</a> <font color="Maroon" title="c11">t1</font>,<font color="Maroon" title="c13">n</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2">(<span class="default"><a href="scm_comp.html#K15" title="SCM_COMP:func.15">SCM-Compile</a> <font color="Maroon" title="c12">t2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c13">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1">(<span class="default"><a href="scm_comp.html#K14" title="SCM_COMP:func.14">Selfwork</a> <font color="Maroon" title="c10">nt</font>,<font color="Maroon" title="c13">n</font></span>)</span>
 
<b>by </b><i><a class="txt" href="scm_comp.html#E3:22"><i><font color="Green" title="E17">A1</font></i></a></i>;<br/>
<b>hence </b><a NAME="E7:22"/>
 <a href="scm_comp.html#K15" title="SCM_COMP:func.15">SCM-Compile</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">nt</font> <a href="scm_comp.html#K2" title="SCM_COMP:func.2">-tree</a> <font color="Maroon" title="c11">t1</font>,<font color="Maroon" title="c12">t2</font></span>)</span>,<font color="Maroon" title="c13">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scm_comp.html#K15" title="SCM_COMP:func.15">SCM-Compile</a> <font color="Maroon" title="c11">t1</font>,<font color="Maroon" title="c13">n</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2">(<span class="default"><a href="scm_comp.html#K15" title="SCM_COMP:func.15">SCM-Compile</a> <font color="Maroon" title="c12">t2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c13">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1">(<span class="default"><a href="scm_comp.html#K14" title="SCM_COMP:func.14">Selfwork</a> <font color="Maroon" title="c10">nt</font>,<font color="Maroon" title="c13">n</font></span>)</span>
 <b>by </b><i><a class="txt" href="scm_comp.html#E3:22"><i><font color="Green" title="E17">A1</font></i></a>, <a class="ref" href="scm_comp.html#D11" target="_self" title="SCM_COMP:def.11">Def11</a>, <a class="txt" href="scm_comp.html#E27"><i><font color="Green" title="E14">Lm4</font></i></a></i>;<br/>


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