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<span class="kw">let </span><font color="Maroon" title="c7">t</font> be   <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>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  holds   <a href="scm_comp.html#K15" title="SCM_COMP:func.15">SCM-Compile</a> (<span class="p1">(<span class="default"><a href="scm_comp.html#K3" title="SCM_COMP:func.3">root-tree</a> <font color="Maroon" title="c7">t</font></span>)</span>,<font color="Olive" title="b1">n</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_3.html#K10" title="AMI_3:func.10">dl.</a> <font color="Olive" title="b1">n</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">:=</a> <span class="p3">(<span class="default"><a href="scm_comp.html#K4" title="SCM_COMP:func.4">@</a> <font color="Maroon" title="c7">t</font></span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c8">n</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="scm_comp.html#K15" title="SCM_COMP:func.15">SCM-Compile</a> (<span class="p1">(<span class="default"><a href="scm_comp.html#K3" title="SCM_COMP:func.3">root-tree</a> <font color="Maroon" title="c7">t</font></span>)</span>,<font color="Maroon" title="c8">n</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_3.html#K10" title="AMI_3:func.10">dl.</a> <font color="Maroon" title="c8">n</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">:=</a> <span class="p3">(<span class="default"><a href="scm_comp.html#K4" title="SCM_COMP:func.4">@</a> <font color="Maroon" title="c7">t</font></span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span><br/>



<span class="kw">consider </span><font color="Maroon" title="c9">g</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">sequence</a> of <span class="p1">(<span class="default"> the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">InstructionsF</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="E2:20"/><span class="lab"><font color="Green" title="E13">A1</font></span>: 
<font color="Maroon" title="c9">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scm_comp.html#K14" title="SCM_COMP:func.14">SCM-Compile</a> <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="Maroon" title="c7">t</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E3:20"/><span class="lab"><font color="Green" title="E14">A2</font></span>: 
 for <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds  <font color="Maroon" title="c9">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_3.html#K10" title="AMI_3:func.10">dl.</a> <font color="Olive" title="b1">n</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">:=</a> <span class="p3">(<span class="default"><a href="scm_comp.html#K4" title="SCM_COMP:func.4">@</a> <font color="Maroon" title="c7">t</font></span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scm_comp.html#D11" target="_self" onmouseover="rs('scm_comp/D11')" onmouseout="rh()">Def11</a></span>;<br/>
<span class="kw">thus </span><a NAME="E4:20"/>
 <a href="scm_comp.html#K15" title="SCM_COMP:func.15">SCM-Compile</a> (<span class="p1">(<span class="default"><a href="scm_comp.html#K3" title="SCM_COMP:func.3">root-tree</a> <font color="Maroon" title="c7">t</font></span>)</span>,<font color="Maroon" title="c8">n</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_3.html#K10" title="AMI_3:func.10">dl.</a> <font color="Maroon" title="c8">n</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">:=</a> <span class="p3">(<span class="default"><a href="scm_comp.html#K4" title="SCM_COMP:func.4">@</a> <font color="Maroon" title="c7">t</font></span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:20"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="txt" href="#E3:20"><span class="lab"><font color="Green" title="E14">A2</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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