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<span class="kw">let </span><font color="Maroon" title="c7">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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">t1</font>, <font color="Olive" title="b2">t2</font> being   <a href="scm_comp.html#NM1" title="SCM_COMP:NM.1">bin-term</a><br/>  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="numbers.html#K5" title="NUMBERS:func.5">NAT</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="b1">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="b2">t2</font> &amp; <font color="Maroon" title="c7">nt</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a> <span class="p1"><a href="pre_poly.html#K4" title="PRE_POLY:func.4">&lt;*</a><span class="default"><font color="Olive" title="b4">rtl</font>,<font color="Olive" title="b5">rtr</font></span><a href="pre_poly.html#K4" title="PRE_POLY:func.4">*&gt;</a></span> holds <br/> <a href="scm_comp.html#K16" title="SCM_COMP:func.16">SCM-Compile</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c7">nt</font> <a href="scm_comp.html#K2" title="SCM_COMP:func.2">-tree</a> (<font color="Olive" title="b1">t1</font>,<font color="Olive" title="b2">t2</font>)</span>)</span>,<font color="Olive" title="b3">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#K16" title="SCM_COMP:func.16">SCM-Compile</a> (<font color="Olive" title="b1">t1</font>,<font color="Olive" title="b3">n</font>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><a href="scm_comp.html#K16" title="SCM_COMP:func.16">SCM-Compile</a> (<font color="Olive" title="b2">t2</font>,<span class="p3">(<span class="default"><font color="Olive" title="b3">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4: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="c7">nt</font>,<font color="Olive" title="b3">n</font>)</span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c8">t1</font>, <font color="Maroon" title="c9">t2</font> be   <a href="scm_comp.html#NM1" title="SCM_COMP:NM.1">bin-term</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  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> <br/>  for <font color="Olive" title="b2">rtl</font>, <font color="Olive" title="b3">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="b2">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="c8">t1</font> &amp; <font color="Olive" title="b3">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="c9">t2</font> &amp; <font color="Maroon" title="c7">nt</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a> <span class="p1"><a href="pre_poly.html#K4" title="PRE_POLY:func.4">&lt;*</a><span class="default"><font color="Olive" title="b2">rtl</font>,<font color="Olive" title="b3">rtr</font></span><a href="pre_poly.html#K4" title="PRE_POLY:func.4">*&gt;</a></span> holds <br/> <a href="scm_comp.html#K16" title="SCM_COMP:func.16">SCM-Compile</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c7">nt</font> <a href="scm_comp.html#K2" title="SCM_COMP:func.2">-tree</a> (<font color="Maroon" title="c8">t1</font>,<font color="Maroon" title="c9">t2</font>)</span>)</span>,<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"><a href="scm_comp.html#K16" title="SCM_COMP:func.16">SCM-Compile</a> (<font color="Maroon" title="c8">t1</font>,<font color="Olive" title="b1">n</font>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><a href="scm_comp.html#K16" title="SCM_COMP:func.16">SCM-Compile</a> (<font color="Maroon" title="c9">t2</font>,<span class="p3">(<span class="default"><font color="Olive" title="b1">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4: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="c7">nt</font>,<font color="Olive" title="b1">n</font>)</span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c10">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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">rtl</font>, <font color="Olive" title="b2">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="b1">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="c8">t1</font> &amp; <font color="Olive" title="b2">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="c9">t2</font> &amp; <font color="Maroon" title="c7">nt</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a> <span class="p1"><a href="pre_poly.html#K4" title="PRE_POLY:func.4">&lt;*</a><span class="default"><font color="Olive" title="b1">rtl</font>,<font color="Olive" title="b2">rtr</font></span><a href="pre_poly.html#K4" title="PRE_POLY:func.4">*&gt;</a></span> holds <br/> <a href="scm_comp.html#K16" title="SCM_COMP:func.16">SCM-Compile</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c7">nt</font> <a href="scm_comp.html#K2" title="SCM_COMP:func.2">-tree</a> (<font color="Maroon" title="c8">t1</font>,<font color="Maroon" title="c9">t2</font>)</span>)</span>,<font color="Maroon" title="c10">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#K16" title="SCM_COMP:func.16">SCM-Compile</a> (<font color="Maroon" title="c8">t1</font>,<font color="Maroon" title="c10">n</font>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><a href="scm_comp.html#K16" title="SCM_COMP:func.16">SCM-Compile</a> (<font color="Maroon" title="c9">t2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c10">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4: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="c7">nt</font>,<font color="Maroon" title="c10">n</font>)</span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c11">rtl</font>, <font color="Maroon" title="c12">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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c11">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="c8">t1</font> &amp; <font color="Maroon" title="c12">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="c9">t2</font> &amp; <font color="Maroon" title="c7">nt</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a> <span class="p1"><a href="pre_poly.html#K4" title="PRE_POLY:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c11">rtl</font>,<font color="Maroon" title="c12">rtr</font></span><a href="pre_poly.html#K4" title="PRE_POLY:func.4">*&gt;</a></span> implies  <a href="scm_comp.html#K16" title="SCM_COMP:func.16">SCM-Compile</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c7">nt</font> <a href="scm_comp.html#K2" title="SCM_COMP:func.2">-tree</a> (<font color="Maroon" title="c8">t1</font>,<font color="Maroon" title="c9">t2</font>)</span>)</span>,<font color="Maroon" title="c10">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#K16" title="SCM_COMP:func.16">SCM-Compile</a> (<font color="Maroon" title="c8">t1</font>,<font color="Maroon" title="c10">n</font>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><a href="scm_comp.html#K16" title="SCM_COMP:func.16">SCM-Compile</a> (<font color="Maroon" title="c9">t2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c10">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4: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="c7">nt</font>,<font color="Maroon" title="c10">n</font>)</span>)</span> )</span><br/>







<span class="kw">assume </span><a NAME="E1:21"/><span class="lab"><font color="Green" title="E14">A1</font></span>: 
( <font color="Maroon" title="c11">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="c8">t1</font> &amp; <font color="Maroon" title="c12">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="c9">t2</font> &amp; <font color="Maroon" title="c7">nt</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a> <span class="p1"><a href="pre_poly.html#K4" title="PRE_POLY:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c11">rtl</font>,<font color="Maroon" title="c12">rtr</font></span><a href="pre_poly.html#K4" title="PRE_POLY:func.4">*&gt;</a></span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="scm_comp.html#K16" title="SCM_COMP:func.16">SCM-Compile</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c7">nt</font> <a href="scm_comp.html#K2" title="SCM_COMP:func.2">-tree</a> (<font color="Maroon" title="c8">t1</font>,<font color="Maroon" title="c9">t2</font>)</span>)</span>,<font color="Maroon" title="c10">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#K16" title="SCM_COMP:func.16">SCM-Compile</a> (<font color="Maroon" title="c8">t1</font>,<font color="Maroon" title="c10">n</font>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><a href="scm_comp.html#K16" title="SCM_COMP:func.16">SCM-Compile</a> (<font color="Maroon" title="c9">t2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c10">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4: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="c7">nt</font>,<font color="Maroon" title="c10">n</font>)</span>)</span></span><br/>

<span class="kw">consider </span><font color="Maroon" title="c13">g</font>, <font color="Maroon" title="c14">f1</font>, <font color="Maroon" title="c15">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>,<span class="p1">(<span class="default"> the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> <a href="afinsq_1.html#K8" title="AFINSQ_1:func.8">^omega</a></span>)</span><span class="kw"> such that </span><br/><a NAME="E3:21"/><span class="lab"><font color="Green" title="E15">A2</font></span>: 
<font color="Maroon" title="c13">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scm_comp.html#K15" title="SCM_COMP:func.15">SCM-Compile</a> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">nt</font> <a href="scm_comp.html#K2" title="SCM_COMP:func.2">-tree</a> (<font color="Maroon" title="c8">t1</font>,<font color="Maroon" title="c9">t2</font>)</span>)</span>
 <span class="kw">and </span><br/><a NAME="E4:21"/><span class="lab"><font color="Green" title="E16">A3</font></span>: 
<font color="Maroon" title="c14">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scm_comp.html#K15" title="SCM_COMP:func.15">SCM-Compile</a> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">t1</font>
 <span class="kw">and </span><br/><a NAME="E5:21"/><span class="lab"><font color="Green" title="E17">A4</font></span>: 
<font color="Maroon" title="c15">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scm_comp.html#K15" title="SCM_COMP:func.15">SCM-Compile</a> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">t2</font>
 <span class="kw">and </span><br/><a NAME="E6:21"/><span class="lab"><font color="Green" title="E18">A5</font></span>: 
 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="c13">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="c14">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="afinsq_1.html#K15" title="AFINSQ_1:func.15">^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c15">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#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4: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="c7">nt</font>,<font color="Olive" title="b1">n</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:21"><span class="lab"><font color="Green" title="E14">A1</font></span></a>, <a class="ref" href="scm_comp.html#D11" target="_self" title="SCM_COMP:def.11">Def13</a></span>;<br/>
<span class="kw">thus </span><a NAME="E7:21"/>
 <a href="scm_comp.html#K16" title="SCM_COMP:func.16">SCM-Compile</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c7">nt</font> <a href="scm_comp.html#K2" title="SCM_COMP:func.2">-tree</a> (<font color="Maroon" title="c8">t1</font>,<font color="Maroon" title="c9">t2</font>)</span>)</span>,<font color="Maroon" title="c10">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#K16" title="SCM_COMP:func.16">SCM-Compile</a> (<font color="Maroon" title="c8">t1</font>,<font color="Maroon" title="c10">n</font>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><a href="scm_comp.html#K16" title="SCM_COMP:func.16">SCM-Compile</a> (<font color="Maroon" title="c9">t2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c10">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4: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="c7">nt</font>,<font color="Maroon" title="c10">n</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:21"><span class="lab"><font color="Green" title="E16">A3</font></span></a>, <a class="txt" href="#E5:21"><span class="lab"><font color="Green" title="E17">A4</font></span></a>, <a class="txt" href="#E6:21"><span class="lab"><font color="Green" title="E18">A5</font></span></a>, <a class="txt" href="#E3:21"><span class="lab"><font color="Green" title="E15">A2</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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