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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="firebrick">::  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="memstr_0.html#V2" title="MEMSTR_0:attr.2">IC-Ins-separated</a>   <a href="extpro_1.html#V3" title="EXTPRO_1:attr.3">halting</a>   <a href="extpro_1.html#L1" title="EXTPRO_1:struct.1">AMI-Struct</a> of <font color="Maroon" title="c1">N</font><br/>  for <font color="Olive" title="b2">P</font> being   <a href="compos_1.html#NM2" title="COMPOS_1:NM.2">Instruction-Sequence</a> of <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b3">s</font> being   <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">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="compos_1.html#K3" title="COMPOS_1:func.3">.</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">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="compos_1.html#K2" title="COMPOS_1:func.2">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="extpro_1.html#K6" title="EXTPRO_1:func.6">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="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Olive" title="b2">P</font>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">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="memstr_0.html#V2" title="MEMSTR_0:attr.2">IC-Ins-separated</a>   <a href="extpro_1.html#V3" title="EXTPRO_1:attr.3">halting</a>   <a href="extpro_1.html#L1" title="EXTPRO_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="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">P</font> being   <a href="compos_1.html#NM2" title="COMPOS_1:NM.2">Instruction-Sequence</a> of <font color="Maroon" title="c2">S</font><br/>  for <font color="Olive" title="b2">s</font> being   <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">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="compos_1.html#K3" title="COMPOS_1:func.3">.</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">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="compos_1.html#K2" title="COMPOS_1:func.2">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="extpro_1.html#K6" title="EXTPRO_1:func.6">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="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Olive" title="b1">P</font>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">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   <a href="compos_1.html#NM2" title="COMPOS_1:NM.2">Instruction-Sequence</a> of <font color="Maroon" title="c2">S</font>; <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">s</font> being   <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">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="compos_1.html#K3" title="COMPOS_1:func.3">.</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">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="compos_1.html#K2" title="COMPOS_1:func.2">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="extpro_1.html#K6" title="EXTPRO_1:func.6">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="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c3">P</font>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">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="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <font color="Maroon" title="c2">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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="compos_1.html#K3" title="COMPOS_1:func.3">.</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">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="compos_1.html#K2" title="COMPOS_1:func.2">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="extpro_1.html#K6" title="EXTPRO_1:func.6">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="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c3">P</font>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">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="E2:27"/><span class="lab"><font color="Green" title="E13">A1</font></span>: 
<font color="Maroon" title="c3">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">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="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <font color="Maroon" title="c2">S</font>
 ; <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">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="extpro_1.html#K6" title="EXTPRO_1:func.6">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="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c3">P</font>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">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="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="extpro_1.html#K6" title="EXTPRO_1:func.6">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="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c3">P</font>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">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="E3:27"/><span class="lab"><font color="Green" title="E14">A2</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#D2" title="PARTFUN1:def.2">PARTFUN1:def 2</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">s9</font> =  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">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="E4:27"/><span class="lab"><font color="Green" title="E15">A3</font></span>: 
 <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<font color="Maroon" title="c3">P</font>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">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="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <font color="Maroon" title="c2">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:27"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="txt" href="#E3:27"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="ref" href="partfun1.html#D6" title="PARTFUN1:def.6">PARTFUN1:def 6</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="27_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="E1:27_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="27_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:27_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="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="extpro_1.html#K6" title="EXTPRO_1:func.6">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="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c3">P</font>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">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="E3:27_1_1_1"/><span class="lab"><font color="Green" title="E16">A4</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#D12" title="ORDINAL1:def.12">ORDINAL1:def 12</a></span>;<br/><a NAME="E5:27_1_1_1"/><span class="lab"><font color="Green" title="E17">A5</font></span>: 
 <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">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="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c3">P</font>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">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="#E3:27_1_1_1"><span class="lab"><font color="Green" title="E16">A4</font></span></a>, <a class="ref" href="extpro_1.html#T4" target="_self" title="EXTPRO_1:th.4">Th5</a></span>;<br/><a NAME="E6:27_1_1_1"/><span class="lab"><font color="Green" title="E18">A6</font></span>: 
<font color="Maroon" title="c3">P</font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a>  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">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="#E4:27"><span class="lab"><font color="Green" title="E15">A3</font></span></a>, <a class="txt" href="#E5:27_1_1_1"><span class="lab"><font color="Green" title="E17">A5</font></span></a>, <a class="ref" href="extpro_1.html#D8" target="_self" title="EXTPRO_1:def.8">Def7</a>, <a class="txt" href="#E3:27"><span class="lab"><font color="Green" title="E14">A2</font></span></a></span>;<br/><span class="kw">thus </span> <a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>) = 
 <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">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="#E2:27"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="ref" href="extpro_1.html#T7" target="_self" title="EXTPRO_1:th.7">Th8</a></span>
<br/>.= 
 <a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c3">P</font>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">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="#E4:27"><span class="lab"><font color="Green" title="E15">A3</font></span></a>, <a class="txt" href="#E5:27_1_1_1"><span class="lab"><font color="Green" title="E17">A5</font></span></a>, <a class="txt" href="#E6:27_1_1_1"><span class="lab"><font color="Green" title="E18">A6</font></span></a>, <a class="ref" href="extpro_1.html#D9" target="_self" title="EXTPRO_1:def.9">Def8</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="27_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:27_1_1_2"/><span class="lab"><font color="Green" title="E16">A7</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="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="extpro_1.html#K6" title="EXTPRO_1:func.6">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="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c3">P</font>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">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="E2:27_1_1_2"/><span class="lab"><font color="Green" title="E17">A8</font></span>: 
 <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c3">P</font>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">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="extpro_1.html#K5" title="EXTPRO_1:func.5">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="extpro_1.html#T2" target="_self" title="EXTPRO_1:th.2">Th3</a></span>;<br/><a NAME="E3:27_1_1_2"/><span class="lab"><font color="Green" title="E18">A9</font></span>: 
 <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">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="extpro_1.html#K5" title="EXTPRO_1:func.5">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="#E4:27"><span class="lab"><font color="Green" title="E15">A3</font></span></a>, <a class="txt" href="#E1:27_1_1_2"><span class="lab"><font color="Green" title="E16">A7</font></span></a>, <a class="ref" href="extpro_1.html#T5" target="_self" title="EXTPRO_1:th.5">Th6</a></span>;<br/><a NAME="E4:27_1_1_2"/><span class="lab"><font color="Green" title="E19">A10</font></span>: 
<font color="Maroon" title="c3">P</font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a>  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">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="extpro_1.html#D8" target="_self" title="EXTPRO_1:def.8">Def7</a>, <a class="txt" href="#E3:27"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="txt" href="#E3:27_1_1_2"><span class="lab"><font color="Green" title="E18">A9</font></span></a>, <a class="txt" href="#E4:27"><span class="lab"><font color="Green" title="E15">A3</font></span></a>, <a class="txt" href="#E2:27_1_1_2"><span class="lab"><font color="Green" title="E17">A8</font></span></a></span>;<br/><span class="kw">thus </span> <a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>) = 
 <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">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="#E2:27"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="ref" href="extpro_1.html#T7" target="_self" title="EXTPRO_1:th.7">Th8</a></span>
<br/>.= 
 <a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c3">P</font>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">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="#E4:27"><span class="lab"><font color="Green" title="E15">A3</font></span></a>, <a class="txt" href="#E3:27_1_1_2"><span class="lab"><font color="Green" title="E18">A9</font></span></a>, <a class="txt" href="#E2:27_1_1_2"><span class="lab"><font color="Green" title="E17">A8</font></span></a>, <a class="txt" href="#E4:27_1_1_2"><span class="lab"><font color="Green" title="E19">A10</font></span></a>, <a class="ref" href="extpro_1.html#D9" target="_self" title="EXTPRO_1:def.9">Def8</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/></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="E6:27"/>
 <a href="extpro_1.html#K6" title="EXTPRO_1:func.6">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="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c3">P</font>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">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="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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