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<span class="kw">let </span><font color="Maroon" title="c2">P</font> be   <a href="compos_1.html#NM2" title="COMPOS_1:NM.2">Instruction-Sequence</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</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">s</font> being   <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="memstr_0.html#V5" title="MEMSTR_0:attr.5">-started</a>  <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a><br/>  for <font color="Olive" title="b2">I</font> being   <a href="scmpds_4.html#V2" title="SCMPDS_4:attr.2">parahalting</a>  <a href="compos_1.html#NM4" title="COMPOS_1:NM.4">Program</a> of <br/>  for <font color="Olive" title="b3">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b3">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Olive" title="b2">I</font></span>)</span></span>)</span>,<font color="Olive" title="b1">s</font>) holds <br/> <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Olive" title="b2">I</font></span>)</span></span>)</span>,<font color="Olive" title="b1">s</font>,<font color="Olive" title="b3">k</font>)</span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b2">I</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">s</font> be   <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="memstr_0.html#V5" title="MEMSTR_0:attr.5">-started</a>  <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</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">I</font> being   <a href="scmpds_4.html#V2" title="SCMPDS_4:attr.2">parahalting</a>  <a href="compos_1.html#NM4" title="COMPOS_1:NM.4">Program</a> of <br/>  for <font color="Olive" title="b2">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b2">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Olive" title="b1">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>) holds <br/> <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Olive" title="b1">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>,<font color="Olive" title="b2">k</font>)</span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b1">I</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">I</font> be   <a href="scmpds_4.html#V2" title="SCMPDS_4:attr.2">parahalting</a>  <a href="compos_1.html#NM4" title="COMPOS_1:NM.4">Program</a> of ; <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">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b1">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>) holds <br/> <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>,<font color="Olive" title="b1">k</font>)</span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c4">I</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">k</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">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"> ( <font color="Maroon" title="c5">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>) implies  <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c4">I</font> )</span><br/>







<span class="kw">set </span><font color="Maroon" title="c6">ss</font> = <font color="Maroon" title="c3">s</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">PP</font> = <font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">m</font> =  <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c9">Sk</font> =  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c5">k</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c10">Ik</font> =  <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span>;<br/>
<a NAME="E1:44"/><span class="lab"><font color="Green" title="E16">A1</font></span>: 
 <a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T25" onmouseover="rs('funct_4/T25')" onmouseout="rh()">FUNCT_4:25</a></span>;<br/>
<a NAME="E2:44"/><span class="kw">then </span><span class="lab"><font color="Green" title="E17">A2</font></span>: 
<font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Maroon" title="c3">s</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_4.html#D7" onmouseover="rs('scmpds_4/D7')" onmouseout="rh()">SCMPDS_4:def 7</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c11">n</font> =  <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span> as   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> ;<br/>
<a NAME="E4:44"/><span class="lab"><font color="Green" title="E18">A3</font></span>: 
 <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:44"><span class="lab"><font color="Green" title="E16">A1</font></span></a>, <a class="ref" href="scmpds_4.html#D6" onmouseover="rs('scmpds_4/D6')" onmouseout="rh()">SCMPDS_4:def 6</a></span>;<br/>
<a NAME="E5:44"/><span class="lab"><font color="Green" title="E19">A4</font></span>: 
 <a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T25" onmouseover="rs('funct_4/T25')" onmouseout="rh()">FUNCT_4:25</a></span>;<br/>
<span class="kw">assume </span><a NAME="E6:44"/><span class="lab"><font color="Green" title="E20">A5</font></span>: 
<font color="Maroon" title="c5">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>)
 ; <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="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c4">I</font></span><br/>

<div><span class="lab"><font color="Green" title="E21">A6</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="44_1"><span class="kw">now </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">  not <font color="Maroon" title="c11">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">I</font></span></a><div class="add"><span class="kw">assume </span><a NAME="E1:44_1"/><span class="lab"><font color="Green" title="E22">A7</font></span>: 
<font color="Maroon" title="c11">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">I</font>
 ; <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"> contradiction</span><br/><a NAME="E2:44_1"/><span class="lab"><font color="Green" title="E23">A8</font></span>: 
 <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#K4" title="COMPOS_1:func.4">Stop</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="compos_1.html#T3" onmouseover="rs('compos_1/T3')" onmouseout="rh()">COMPOS_1:3</a></span>;<br/><a NAME="E3:44_1"/><span class="lab"><font color="Green" title="E24">A9</font></span>: 
<span class="p1">(<span class="default"><a href="compos_1.html#K4" title="COMPOS_1:func.4">Stop</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>
 ;<br/> <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span>) = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">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="pboole.html#T143" onmouseover="rs('pboole/T143')" onmouseout="rh()">PBOOLE:143</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c11">n</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:44"><span class="lab"><font color="Green" title="E18">A3</font></span></a>, <a class="txt" href="#E5:44"><span class="lab"><font color="Green" title="E19">A4</font></span></a>, <a class="ref" href="grfunc_1.html#T2" onmouseover="rs('grfunc_1/T2')" onmouseout="rh()">GRFUNC_1:2</a></span>
<br/>.= 
 <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:44_1"><span class="lab"><font color="Green" title="E22">A7</font></span></a>, <a class="txt" href="#E3:44_1"><span class="lab"><font color="Green" title="E24">A9</font></span></a>, <a class="txt" href="#E2:44_1"><span class="lab"><font color="Green" title="E23">A8</font></span></a>, <a class="ref" href="afinsq_1.html#D3" onmouseover="rs('afinsq_1/D3')" onmouseout="rh()">AFINSQ_1:def 3</a></span>
;<br/><span class="kw">hence </span><a NAME="E5:44_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:44"><span class="lab"><font color="Green" title="E20">A5</font></span></a>, <a class="txt" href="#E2:44"><span class="lab"><font color="Green" title="E17">A2</font></span></a>, <a class="ref" href="extpro_1.html#D15" onmouseover="rs('extpro_1/D15')" onmouseout="rh()">EXTPRO_1:def 15</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/></div><span class="kw">end;</span></div>
<a NAME="E8:44"/>
 <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="scmpds_5.html#E1"><span class="lab"><font color="Green" title="E1">Lm1</font></span></a>, <a class="ref" href="afinsq_1.html#T17" onmouseover="rs('afinsq_1/T17')" onmouseout="rh()">AFINSQ_1:17</a></span>;<br/>
<a NAME="E9:44"/><span class="kw">then </span>
<font color="Maroon" title="c11">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:44"><span class="lab"><font color="Green" title="E18">A3</font></span></a>, <a class="ref" href="afinsq_1.html#T66" onmouseover="rs('afinsq_1/T66')" onmouseout="rh()">AFINSQ_1:66</a></span>;<br/>
<a NAME="E10:44"/><span class="kw">then </span>
<font color="Maroon" title="c11">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">I</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="int_1.html#T7" onmouseover="rs('int_1/T7')" onmouseout="rh()">INT_1:7</a></span>;<br/>
<a NAME="E11:44"/><span class="kw">then </span>
<font color="Maroon" title="c11">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">I</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:44"><span class="lab"><font color="Green" title="E21">A6</font></span></a>, <a class="ref" href="xxreal_0.html#T1" onmouseover="rs('xxreal_0/T1')" onmouseout="rh()">XXREAL_0:1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E12:44"/>
 <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon" title="c4">I</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c5">k</font>)</span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c4">I</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T66" onmouseover="rs('afinsq_1/T66')" onmouseout="rh()">AFINSQ_1:66</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/>


</div>
