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<span class="kw">let </span><font color="Maroon" title="c1">N</font> be  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="setfam_1.html#V1" title="SETFAM_1:attr.1">with_non-empty_elements</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">S</font> being non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="ami_1.html#V2" title="AMI_1:attr.2">stored-program</a>   <a href="ami_1.html#V4" title="AMI_1:attr.4">halting</a>   <a href="ami_1.html#V5" title="AMI_1:attr.5">IC-Ins-separated</a>   <a href="ami_1.html#V7" title="AMI_1:attr.7">steady-programmed</a>   <a href="ami_1.html#V8" title="AMI_1:attr.8">definite</a>   <a href="ami_1.html#L1" title="AMI_1:struct.1">AMI-Struct</a> of <font color="Maroon" title="c1">N</font><br/> for <font color="Olive" title="b2">P</font> being the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <font color="Olive">b<sub>1</sub></font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <br/> for <font color="Olive" title="b3">s</font> being  <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <font color="Olive" title="b1">S</font>  st  ex <font color="Olive" title="b4">k</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <font color="Olive" title="b2">P</font> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Olive" title="b2">P</font>,<font color="Olive" title="b3">s</font>,<font color="Olive" title="b4">k</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <font color="Olive" title="b1">S</font> holds <br/>for <font color="Olive" title="b4">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds   <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <font color="Olive" title="b2">P</font>,<font color="Olive" title="b3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <font color="Olive" title="b2">P</font>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Olive" title="b2">P</font>,<font color="Olive" title="b3">s</font>,<font color="Olive" title="b4">i</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">S</font> be  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="ami_1.html#V2" title="AMI_1:attr.2">stored-program</a>   <a href="ami_1.html#V4" title="AMI_1:attr.4">halting</a>   <a href="ami_1.html#V5" title="AMI_1:attr.5">IC-Ins-separated</a>   <a href="ami_1.html#V7" title="AMI_1:attr.7">steady-programmed</a>   <a href="ami_1.html#V8" title="AMI_1:attr.8">definite</a>   <a href="ami_1.html#L1" title="AMI_1:struct.1">AMI-Struct</a> of <font color="Maroon" title="c1">N</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">P</font> being the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <font color="Maroon" title="c2">S</font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <br/> for <font color="Olive" title="b2">s</font> being  <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <font color="Maroon" title="c2">S</font>  st  ex <font color="Olive" title="b3">k</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <font color="Olive" title="b1">P</font> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Olive" title="b1">P</font>,<font color="Olive" title="b2">s</font>,<font color="Olive" title="b3">k</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <font color="Maroon" title="c2">S</font> holds <br/>for <font color="Olive" title="b3">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds   <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <font color="Olive" title="b1">P</font>,<font color="Olive" title="b2">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <font color="Olive" title="b1">P</font>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Olive" title="b1">P</font>,<font color="Olive" title="b2">s</font>,<font color="Olive" title="b3">i</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">P</font> be  the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <font color="Maroon" title="c2">S</font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</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="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">s</font> being  <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <font color="Maroon" title="c2">S</font>  st  ex <font color="Olive" title="b2">k</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <font color="Maroon" title="c3">P</font> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Maroon" title="c3">P</font>,<font color="Olive" title="b1">s</font>,<font color="Olive" title="b2">k</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <font color="Maroon" title="c2">S</font> holds <br/>for <font color="Olive" title="b2">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds   <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <font color="Maroon" title="c3">P</font>,<font color="Olive" title="b1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <font color="Maroon" title="c3">P</font>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Maroon" title="c3">P</font>,<font color="Olive" title="b1">s</font>,<font color="Olive" title="b2">i</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">s</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <font color="Maroon" title="c2">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  ex <font color="Olive" title="b1">k</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <font color="Maroon" title="c3">P</font> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Olive" title="b1">k</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <font color="Maroon" title="c2">S</font> implies for <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds   <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <font color="Maroon" title="c3">P</font>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Olive" title="b1">i</font></span>)</span> )</span><br/>







<span class="kw">given </span><font color="Maroon" title="c5">k</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <span class="kw"> such that </span><a NAME="E2:106"/><span class="lab"><font color="Green" title="E29">A1</font></span>: 
<font color="Maroon" title="c3">P</font> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c5">k</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <font color="Maroon" title="c2">S</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds   <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <font color="Maroon" title="c3">P</font>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Olive" title="b1">i</font></span>)</span></span><br/>

<span class="kw">let </span><font color="Maroon" title="c6">i</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">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="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <font color="Maroon" title="c3">P</font>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c6">i</font></span>)</span></span><br/>

<a NAME="E3:106"/><span class="lab"><font color="Green" title="E30">XX</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D4" title="PARTFUN1:def.4">PARTFUN1:def 4</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">s9</font> =  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c5">k</font>;<br/>
<a NAME="E4:106"/>
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c5">k</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:106"><span class="lab"><font color="Green" title="E30">XX</font></span></a></span>;<br/>
<a NAME="E5:106"/><span class="kw">then </span><span class="lab"><font color="Green" title="E31">Y</font></span>: 
<font color="Maroon" title="c3">P</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c5">k</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">P</font> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c5">k</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></span>;<br/>
<a NAME="E6:106"/><span class="lab"><font color="Green" title="E32">A2</font></span>: 
 <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <font color="Maroon" title="c3">P</font>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c5">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <font color="Maroon" title="c2">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:106"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="txt" href="#E5:106"><span class="lab"><font color="Green" title="E31">Y</font></span></a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="106_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="106_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:106_1_1"/>
( <font color="Maroon" title="c6">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c5">k</font> or <font color="Maroon" title="c6">i</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c5">k</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="106_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:106_1_1_1"/>
<font color="Maroon" title="c6">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c5">k</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <font color="Maroon" title="c3">P</font>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c6">i</font></span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c8">j</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><span class="kw"> such that </span><br/><a NAME="E3:106_1_1_1"/><span class="lab"><font color="Green" title="E33">A3</font></span>: 
<font color="Maroon" title="c5">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c8">j</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T10" title="NAT_1:th.10">NAT_1:10</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c9">j</font> = <font color="Maroon" title="c8">j</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></span>;<br/><a NAME="E5:106_1_1_1"/><span class="lab"><font color="Green" title="E34">A4</font></span>: 
 <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c5">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Maroon" title="c3">P</font>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c6">i</font></span>)</span>,<font color="Maroon" title="c9">j</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:106_1_1_1"><span class="lab"><font color="Green" title="E33">A3</font></span></a>, <a class="ref" href="ami_1.html#T51" target="_self" title="AMI_1:th.51">Th51</a></span>;<br/><a NAME="E6:106_1_1_1"/>
 <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <font color="Maroon" title="c3">P</font>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c5">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <font color="Maroon" title="c2">S</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:106"><span class="lab"><font color="Green" title="E32">A2</font></span></a></span>;<br/><a NAME="E7:106_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A5</font></span>: 
<font color="Maroon" title="c3">P</font> <a href="ami_1.html#R1" title="AMI_1:pred.1">halts_on</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c6">i</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:106_1_1_1"><span class="lab"><font color="Green" title="E34">A4</font></span></a>, <a class="ref" href="ami_1.html#D20" target="_self" title="AMI_1:def.20">Def20</a>, <a class="txt" href="#E3:106"><span class="lab"><font color="Green" title="E30">XX</font></span></a></span>;<br/><span class="kw">thus </span> <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font> = 
 <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c5">k</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:106"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="ref" href="ami_1.html#T56" target="_self" title="AMI_1:th.56">Th56</a></span>
<br/>.= 
 <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <font color="Maroon" title="c3">P</font>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c6">i</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:106"><span class="lab"><font color="Green" title="E32">A2</font></span></a>, <a class="txt" href="#E5:106_1_1_1"><span class="lab"><font color="Green" title="E34">A4</font></span></a>, <a class="txt" href="#E7:106_1_1_1"><span class="lab"><font color="Green" title="E35">A5</font></span></a>, <a class="ref" href="ami_1.html#D22" target="_self" title="AMI_1:def.22">Def22</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="106_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:106_1_1_2"/><span class="lab"><font color="Green" title="E33">A6</font></span>: 
<font color="Maroon" title="c6">i</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c5">k</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <font color="Maroon" title="c3">P</font>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c6">i</font></span>)</span></span><br/><div class="add"><a NAME="E2:106_1_1_2"/><span class="lab"><font color="Green" title="E34">A7</font></span>: 
 <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Maroon" title="c3">P</font>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c5">k</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c5">k</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T13" target="_self" title="AMI_1:th.13">Th13</a></span>;<br/><a NAME="E3:106_1_1_2"/><span class="lab"><font color="Green" title="E35">A8</font></span>: 
 <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c5">k</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:106"><span class="lab"><font color="Green" title="E32">A2</font></span></a>, <a class="txt" href="#E1:106_1_1_2"><span class="lab"><font color="Green" title="E33">A6</font></span></a>, <a class="ref" href="ami_1.html#T52" target="_self" title="AMI_1:th.52">Th52</a></span>;<br/><a NAME="E4:106_1_1_2"/><span class="lab"><font color="Green" title="E36">X</font></span>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Maroon" title="c3">P</font>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c5">k</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">P</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:106"><span class="lab"><font color="Green" title="E30">XX</font></span></a></span>;<br/><a NAME="E5:106_1_1_2"/>
 <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <font color="Maroon" title="c3">P</font>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Maroon" title="c3">P</font>,<span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c5">k</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <font color="Maroon" title="c2">S</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:106"><span class="lab"><font color="Green" title="E32">A2</font></span></a>, <a class="txt" href="#E2:106_1_1_2"><span class="lab"><font color="Green" title="E34">A7</font></span></a></span>;<br/><a NAME="E6:106_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A9</font></span>: 
<font color="Maroon" title="c3">P</font> <a href="ami_1.html#R1" title="AMI_1:pred.1">halts_on</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c6">i</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#D20" target="_self" title="AMI_1:def.20">Def20</a>, <a class="txt" href="#E4:106_1_1_2"><span class="lab"><font color="Green" title="E36">X</font></span></a>, <a class="txt" href="#E3:106_1_1_2"><span class="lab"><font color="Green" title="E35">A8</font></span></a></span>;<br/><span class="kw">thus </span> <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font> = 
 <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c5">k</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:106"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="ref" href="ami_1.html#T56" target="_self" title="AMI_1:th.56">Th56</a></span>
<br/>.= 
 <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <font color="Maroon" title="c3">P</font>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c6">i</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:106"><span class="lab"><font color="Green" title="E32">A2</font></span></a>, <a class="txt" href="#E3:106_1_1_2"><span class="lab"><font color="Green" title="E35">A8</font></span></a>, <a class="txt" href="#E2:106_1_1_2"><span class="lab"><font color="Green" title="E34">A7</font></span></a>, <a class="txt" href="#E6:106_1_1_2"><span class="lab"><font color="Green" title="E37">A9</font></span></a>, <a class="ref" href="ami_1.html#D22" target="_self" title="AMI_1:def.22">Def22</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E8:106"/>
 <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <font color="Maroon" title="c3">P</font>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c6">i</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
