<?xml version="1.0"?>
<div class="add">

<span class="kw">thus </span><a NAME="E1:12_1_1"/>
 <a href="extpro_1.html#K1" title="EXTPRO_1:func.1">Trivial-AMI</a> <font color="Maroon" title="c1">N</font> is  <a href="compos_1.html#V7" title="COMPOS_1:attr.7">regular</a> 
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="extpro_1.html#K1" title="EXTPRO_1:func.1">Trivial-AMI</a> <font color="Maroon" title="c1">N</font> is  <a href="compos_1.html#V8" title="COMPOS_1:attr.8">J/A-independent</a> </span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c2">I</font> be   <a href="compos_1.html#NM1" title="COMPOS_1:NM.1">Instruction</a> of <span class="p1">(<span class="default"><a href="extpro_1.html#K1" title="EXTPRO_1:func.1">Trivial-AMI</a> <font color="Maroon" title="c1">N</font></span>)</span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="compos_1.html#D14" title="COMPOS_1:def.14">COMPOS_1:def 14</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">b<sub>1</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   holds <br/>(  not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c2">I</font></span>)</span> or <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p3">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  )</span><br/>

<a NAME="E1:12_1_1_1"/>
 <a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="amistd_2.html#E6"><span class="lab"><font color="Green" title="E6">Lm1</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:12_1_1_1"/>
 for <font color="Olive">b<sub>1</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   holds <br/>(  not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c2">I</font></span>)</span> or <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <span class="p3">(<span class="default"><a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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"> verum</span><br/>


</div><span class="kw">end;</span></div>

<span class="kw">let </span><font color="Maroon" title="c2">T</font> be   <a href="compos_1.html#NM3" title="COMPOS_1:NM.3">InsType</a> of <span class="p1">(<span class="default"><a href="extpro_1.html#K1" title="EXTPRO_1:func.1">Trivial-AMI</a> <font color="Maroon" title="c1">N</font></span>)</span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="compos_1.html#D15" title="COMPOS_1:def.15">COMPOS_1:def 15</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">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <br/>  for <font color="Olive">b<sub>3</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   holds <br/>(  not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <font color="Maroon" title="c2">T</font> or  not <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span> or  not <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c2">T</font>,<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>3</sub></font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <span class="p1">(<span class="default"><a href="extpro_1.html#K1" title="EXTPRO_1:func.1">Trivial-AMI</a> <font color="Maroon" title="c1">N</font></span>)</span> or <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c2">T</font>,<font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <span class="p1">(<span class="default"><a href="extpro_1.html#K1" title="EXTPRO_1:func.1">Trivial-AMI</a> <font color="Maroon" title="c1">N</font></span>)</span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">f1</font>, <font color="Maroon" title="c4">f2</font> be   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</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">b<sub>1</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   holds <br/>(  not <font color="Maroon" title="c3">f1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <font color="Maroon" title="c2">T</font> or  not <font color="Maroon" title="c4">f2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span> or  not <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c3">f1</font>,<font color="Olive">b<sub>1</sub></font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <span class="p1">(<span class="default"><a href="extpro_1.html#K1" title="EXTPRO_1:func.1">Trivial-AMI</a> <font color="Maroon" title="c1">N</font></span>)</span> or <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c4">f2</font>,<font color="Olive">b<sub>1</sub></font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <span class="p1">(<span class="default"><a href="extpro_1.html#K1" title="EXTPRO_1:func.1">Trivial-AMI</a> <font color="Maroon" title="c1">N</font></span>)</span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c5">p</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c3">f1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <font color="Maroon" title="c2">T</font> or  not <font color="Maroon" title="c4">f2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span> or  not <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c3">f1</font>,<font color="Maroon" title="c5">p</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <span class="p1">(<span class="default"><a href="extpro_1.html#K1" title="EXTPRO_1:func.1">Trivial-AMI</a> <font color="Maroon" title="c1">N</font></span>)</span> or <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c4">f2</font>,<font color="Maroon" title="c5">p</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <span class="p1">(<span class="default"><a href="extpro_1.html#K1" title="EXTPRO_1:func.1">Trivial-AMI</a> <font color="Maroon" title="c1">N</font></span>)</span> )</span><br/>





<span class="kw">assume </span><a NAME="E2:12_1_1"/>
<font color="Maroon" title="c3">f1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <font color="Maroon" title="c2">T</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c4">f2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span> or  not <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c3">f1</font>,<font color="Maroon" title="c5">p</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <span class="p1">(<span class="default"><a href="extpro_1.html#K1" title="EXTPRO_1:func.1">Trivial-AMI</a> <font color="Maroon" title="c1">N</font></span>)</span> or <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c4">f2</font>,<font color="Maroon" title="c5">p</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <span class="p1">(<span class="default"><a href="extpro_1.html#K1" title="EXTPRO_1:func.1">Trivial-AMI</a> <font color="Maroon" title="c1">N</font></span>)</span> )</span><br/>

<a NAME="E3:12_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E8">A1</font></span>: 
<font color="Maroon" title="c3">f1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="amistd_2.html#E7"><span class="lab"><font color="Green" title="E7">Lm2</font></span></a></span>;<br/>
<span class="kw">assume </span><a NAME="E4:12_1_1"/><span class="lab"><font color="Green" title="E9">A2</font></span>: 
<font color="Maroon" title="c4">f2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c3">f1</font>,<font color="Maroon" title="c5">p</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <span class="p1">(<span class="default"><a href="extpro_1.html#K1" title="EXTPRO_1:func.1">Trivial-AMI</a> <font color="Maroon" title="c1">N</font></span>)</span> or <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c4">f2</font>,<font color="Maroon" title="c5">p</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <span class="p1">(<span class="default"><a href="extpro_1.html#K1" title="EXTPRO_1:func.1">Trivial-AMI</a> <font color="Maroon" title="c1">N</font></span>)</span> )</span><br/>

<a NAME="E5:12_1_1"/>
 <a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p1">(<span class="default"><a href="compos_1.html#K7" title="COMPOS_1:func.7">JumpParts</a> <font color="Maroon" title="c2">T</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="amistd_2.html#E7"><span class="lab"><font color="Green" title="E7">Lm2</font></span></a>, <a class="ref" href="card_3.html#T106" title="CARD_3:th.106">CARD_3:106</a></span>;<br/>
<a NAME="E6:12_1_1"/><span class="kw">then </span>
( <font color="Maroon" title="c3">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c4">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:12_1_1"><span class="lab"><font color="Green" title="E8">A1</font></span></a>, <a class="txt" href="#E4:12_1_1"><span class="lab"><font color="Green" title="E9">A2</font></span></a>, <a class="ref" href="card_3.html#T10" title="CARD_3:th.10">CARD_3:10</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:12_1_1"/>
(  not <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c3">f1</font>,<font color="Maroon" title="c5">p</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <span class="p1">(<span class="default"><a href="extpro_1.html#K1" title="EXTPRO_1:func.1">Trivial-AMI</a> <font color="Maroon" title="c1">N</font></span>)</span> or <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c4">f2</font>,<font color="Maroon" title="c5">p</font></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <span class="p1">(<span class="default"><a href="extpro_1.html#K1" title="EXTPRO_1:func.1">Trivial-AMI</a> <font color="Maroon" title="c1">N</font></span>)</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/>


</div>
