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<span class="kw">let </span><font color="Maroon" title="c6">s</font> be   <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</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">p</font> being   <a href="compos_1.html#NM2" title="COMPOS_1:NM.2">Instruction-Sequence</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a><br/>  for <font color="Olive" title="b2">I</font> being   <a href="scmfsa7b.html#V1" title="SCMFSA7B:attr.1">good</a>   <a href="scm_halt.html#V2" title="SCM_HALT:attr.2">InitHalting</a>  <a href="compos_1.html#NM5" title="COMPOS_1:NM.5">Program</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a><br/>  for <font color="Olive" title="b3">a</font> being   <a href="sf_mastr.html#NV2" title="SF_MASTR:NV.2">read-write</a>   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>   st  not <font color="Olive" title="b2">I</font> <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">destroys</a> <font color="Olive" title="b3">a</font> &amp; <font color="Maroon" title="c6">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c6">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b3">a</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  holds <br/> <a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Olive" title="b3">a</font>,<span class="p2">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b2">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Olive" title="b3">a</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span> <a href="scmfsa8a.html#R1" title="SCMFSA8A:pred.1">is_pseudo-closed_on</a> <font color="Maroon" title="c6">s</font>,<font color="Olive" title="b1">p</font></span><br/><span class="kw">let </span><font color="Maroon" title="c7">p</font> be   <a href="compos_1.html#NM2" title="COMPOS_1:NM.2">Instruction-Sequence</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</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">I</font> being   <a href="scmfsa7b.html#V1" title="SCMFSA7B:attr.1">good</a>   <a href="scm_halt.html#V2" title="SCM_HALT:attr.2">InitHalting</a>  <a href="compos_1.html#NM5" title="COMPOS_1:NM.5">Program</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a><br/>  for <font color="Olive" title="b2">a</font> being   <a href="sf_mastr.html#NV2" title="SF_MASTR:NV.2">read-write</a>   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>   st  not <font color="Olive" title="b1">I</font> <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">destroys</a> <font color="Olive" title="b2">a</font> &amp; <font color="Maroon" title="c6">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c6">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b2">a</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  holds <br/> <a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Olive" title="b2">a</font>,<span class="p2">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b1">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Olive" title="b2">a</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span> <a href="scmfsa8a.html#R1" title="SCMFSA8A:pred.1">is_pseudo-closed_on</a> <font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c7">p</font></span><br/><span class="kw">let </span><font color="Maroon" title="c8">I</font> be   <a href="scmfsa7b.html#V1" title="SCMFSA7B:attr.1">good</a>   <a href="scm_halt.html#V2" title="SCM_HALT:attr.2">InitHalting</a>  <a href="compos_1.html#NM5" title="COMPOS_1:NM.5">Program</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</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">a</font> being   <a href="sf_mastr.html#NV2" title="SF_MASTR:NV.2">read-write</a>   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>   st  not <font color="Maroon" title="c8">I</font> <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">destroys</a> <font color="Olive" title="b1">a</font> &amp; <font color="Maroon" title="c6">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c6">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b1">a</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  holds <br/> <a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Olive" title="b1">a</font>,<span class="p2">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Olive" title="b1">a</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span> <a href="scmfsa8a.html#R1" title="SCMFSA8A:pred.1">is_pseudo-closed_on</a> <font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c7">p</font></span><br/><span class="kw">let </span><font color="Maroon" title="c9">a</font> be   <a href="sf_mastr.html#NV2" title="SF_MASTR:NV.2">read-write</a>   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</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="c8">I</font> <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">destroys</a> <font color="Maroon" title="c9">a</font> &amp; <font color="Maroon" title="c6">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c6">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">a</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies  <a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span> <a href="scmfsa8a.html#R1" title="SCMFSA8A:pred.1">is_pseudo-closed_on</a> <font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c7">p</font> )</span><br/>







<span class="kw">set </span><font color="Maroon" title="c10">P</font> =  <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>);<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c11">I1</font> = <font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span> as   <a href="scm_halt.html#V2" title="SCM_HALT:attr.2">InitHalting</a>  <a href="compos_1.html#NM5" title="COMPOS_1:NM.5">Program</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c12">i</font> = <font color="Maroon" title="c9">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c11">I1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span>;<br/>
<span class="kw">defpred </span><font color="Maroon">S<sub>1</sub></font>[  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>] <span class="kw">means </span> for <font color="Olive" title="b1">s</font> being   <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a><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 <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  st <font color="Olive" title="b1">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Olive" title="b1">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> $1 &amp; <font color="Olive" title="b1">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">a</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  holds <br/>( <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="Olive" title="b2">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Olive" title="b1">s</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Olive" title="b2">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Olive" title="b1">s</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">a</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 &amp; <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="Olive" title="b2">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Olive" title="b1">s</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Olive" title="b2">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Olive" title="b1">s</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp;  ex <font color="Olive" title="b3">k</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <br/>(  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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="Olive" title="b2">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Olive" title="b1">s</font></span>)</span>,<font color="Olive" title="b3">k</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span> &amp; (  for <font color="Olive" title="b4">n</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Olive" title="b4">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b3">k</font> holds <br/> <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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="Olive" title="b2">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Olive" title="b1">s</font></span>)</span>,<font color="Olive" title="b4">n</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> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span> ) ) );<br/>
<span class="kw">assume </span><a NAME="E2:84"/><span class="lab"><font color="Green" title="E60">A1</font></span>: 
 not <font color="Maroon" title="c8">I</font> <a href="scmfsa7b.html#R4" title="SCMFSA7B:pred.4">destroys</a> <font color="Maroon" title="c9">a</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="c6">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or  not <font color="Maroon" title="c6">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">a</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or  <a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span> <a href="scmfsa8a.html#R1" title="SCMFSA8A:pred.1">is_pseudo-closed_on</a> <font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c7">p</font> )</span><br/>

<a NAME="E3:84"/><span class="lab"><font color="Green" title="E61">A2</font></span>: 
 for <font color="Olive" title="b1">k</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="84_1"><span class="kw">proof </span></a><div class="add">

<div><span class="lab"><font color="Green" title="E62">A3</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="84_1_1"><span class="kw">now </span></a><div class="add"><a NAME="E1:84_1_1"/><span class="lab"><font color="Green" title="E63">A4</font></span>: 
(  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#K16" title="COMPOS_1:func.16">Macro</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c11">I1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="compos_1.html#K16" title="COMPOS_1:func.16">Macro</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c11">I1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="compos_1.html#T58" title="COMPOS_1:th.58">COMPOS_1:58</a>, <a class="ref" href="compos_1.html#T60" title="COMPOS_1:th.60">COMPOS_1:60</a></span>;<br/> <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>) = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c9">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c11">I1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <font color="Maroon" title="c11">I1</font></span>)</span> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p0">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <span class="p2">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span></span>)</span> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <span class="p1">(<span class="default"><a href="compos_1.html#K6" title="COMPOS_1:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa8b.html#D1" title="SCMFSA8B:def.1">SCMFSA8B:def 1</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c11">I1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c11">I1</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <span class="p4">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <span class="p2">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span></span>)</span> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <span class="p1">(<span class="default"><a href="compos_1.html#K6" title="COMPOS_1:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa6a.html#T29" title="SCMFSA6A:th.29">SCMFSA6A:29</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c11">I1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c11">I1</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <span class="p4">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <span class="p1">(<span class="default"><a href="compos_1.html#K6" title="COMPOS_1:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa6a.html#T29" title="SCMFSA6A:th.29">SCMFSA6A:29</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c11">I1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span> <a href="scmfsa6a.html#K5" title="SCMFSA6A:func.5">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c11">I1</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <span class="p4">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span></span>)</span> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <span class="p2">(<span class="default"><a href="compos_1.html#K6" title="COMPOS_1:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa6a.html#T29" title="SCMFSA6A:th.29">SCMFSA6A:29</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="compos_1.html#K16" title="COMPOS_1:func.16">Macro</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c11">I1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c11">I1</font> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <span class="p4">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span></span>)</span> <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">';'</a> <span class="p2">(<span class="default"><a href="compos_1.html#K6" title="COMPOS_1:func.6">Stop</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span></span>)</span>

;<br/><span class="kw">hence </span><span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> = 
<span class="p1">(<span class="default"><a href="compos_1.html#K16" title="COMPOS_1:func.16">Macro</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c11">I1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.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="#E1:84_1_1"><span class="lab"><font color="Green" title="E63">A4</font></span></a>, <a class="ref" href="scmfsa6a.html#T15" title="SCMFSA6A:th.15">SCMFSA6A:15</a></span>
<br/>.= 
<font color="Maroon" title="c9">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c11">I1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="compos_1.html#T58" title="COMPOS_1:th.58">COMPOS_1:58</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> &amp;  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c11">I1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p2">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p3">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c11">I1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> &amp; <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c11">I1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span> )</span><br/><span class="kw">hence </span><a NAME="E4:84_1_1"/>
<span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c11">I1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p2">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p3">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c11">I1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> &amp; <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c11">I1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span> )</span><br/><span class="lab"><font color="Green" title="E64">A5</font></span>:  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c11">I1</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa8b.html#T11" title="SCMFSA8B:th.11">SCMFSA8B:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c11">I1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa8a.html#T15" title="SCMFSA8A:th.15">SCMFSA8A:15</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c11">I1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2

;<br/><span class="kw">hence </span><a NAME="E6:84_1_1"/>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T66" title="AFINSQ_1:th.66">AFINSQ_1:66</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c11">I1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p2">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p3">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c11">I1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> &amp; <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c11">I1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span> )</span><br/> <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span> = 
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p3">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#T62" title="CARD_1:th.62">CARD_1:62</a></span>
<br/>.= 
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T99" title="FUNCT_4:th.99">FUNCT_4:99</a></span>
<br/>.= 
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#T62" title="CARD_1:th.62">CARD_1:62</a></span>
;<br/><a NAME="E8:84_1_1"/><span class="kw">then </span>
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c11">I1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default">3 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:84_1_1"><span class="lab"><font color="Green" title="E64">A5</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E9:84_1_1"/>
<span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c11">I1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p2">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p3">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa8c.html#T83" title="SCMFSA8C:th.83">SCMFSA8C:83</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c11">I1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> &amp; <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c11">I1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span> )</span><br/><span class="kw">hence </span><a NAME="E10:84_1_1"/>
<span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c11">I1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c11">I1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span><br/><div><span class="kw">hereby </span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span>
<div class="add"><a NAME="E1:84_1_1_5"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c11">I1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:84_1_1"><span class="lab"><font color="Green" title="E64">A5</font></span></a>, <a class="ref" href="xreal_1.html#T6" title="XREAL_1:th.6">XREAL_1:6</a></span>;<br/><span class="kw">hence </span><a NAME="E2:84_1_1_5"/>
<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c11">I1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T66" title="AFINSQ_1:th.66">AFINSQ_1:66</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>
<span class="kw">let </span><font color="Maroon" title="c13">k</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">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"> ( <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c13">k</font>] implies <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c13">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1] )</span><br/>

<span class="kw">assume </span><a NAME="E2:84_1"/><span class="lab"><font color="Green" title="E63">A6</font></span>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c13">k</font>]
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c13">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1]</span><br/>

<span class="kw">let </span><font color="Maroon" title="c14">ss</font> be   <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</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">p</font> being   <a href="compos_1.html#NM2" title="COMPOS_1:NM.2">Instruction-Sequence</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  st <font color="Maroon" title="c14">ss</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c14">ss</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <font color="Maroon" title="c14">ss</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">a</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  holds <br/>( <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="Olive" title="b1">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Olive" title="b1">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">ss</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">a</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 &amp; <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="Olive" title="b1">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Olive" title="b1">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp;  ex <font color="Olive" title="b2">k</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <br/>(  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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="Olive" title="b1">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<font color="Olive" title="b2">k</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span> &amp; (  for <font color="Olive" title="b3">n</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Olive" title="b3">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b2">k</font> holds <br/> <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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="Olive" title="b1">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<font color="Olive" title="b3">n</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> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span> ) ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c15">pp</font> be   <a href="compos_1.html#NM2" title="COMPOS_1:NM.2">Instruction-Sequence</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c14">ss</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c14">ss</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <font color="Maroon" title="c14">ss</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">a</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies ( <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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">ss</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">a</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 &amp; <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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp;  ex <font color="Olive" title="b1">k</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <br/>(  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<font color="Olive" title="b1">k</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span> &amp; (  for <font color="Olive" title="b2">n</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Olive" title="b2">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b1">k</font> holds <br/> <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<font color="Olive" title="b2">n</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> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span> ) ) ) )</span><br/>



<span class="kw">assume </span><a NAME="E3:84_1"/>
<font color="Maroon" title="c14">ss</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ; <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="c14">ss</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 or  not <font color="Maroon" title="c14">ss</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">a</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or ( <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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">ss</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">a</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 &amp; <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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp;  ex <font color="Olive" title="b1">k</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <br/>(  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<font color="Olive" title="b1">k</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span> &amp; (  for <font color="Olive" title="b2">n</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Olive" title="b2">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b1">k</font> holds <br/> <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<font color="Olive" title="b2">n</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> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span> ) ) ) )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c16">s2</font> =  <a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c17">p2</font> = <font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>;<br/>
<a NAME="E4:84_1"/><span class="lab"><font color="Green" title="E64">A7</font></span>: 
 <a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T25" title="FUNCT_4:th.25">FUNCT_4:25</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c18">s1</font> =  <a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c19">p1</font> = <font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span>;<br/>
<span class="kw">assume </span><a NAME="E5:84_1"/><span class="lab"><font color="Green" title="E65">A8</font></span>: 
<font color="Maroon" title="c14">ss</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 ; <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="c14">ss</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">a</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or ( <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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">ss</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">a</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 &amp; <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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp;  ex <font color="Olive" title="b1">k</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <br/>(  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<font color="Olive" title="b1">k</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span> &amp; (  for <font color="Olive" title="b2">n</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Olive" title="b2">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b1">k</font> holds <br/> <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<font color="Olive" title="b2">n</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> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span> ) ) ) )</span><br/>

<span class="lab"><font color="Green" title="E66">A9</font></span>:  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p3">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>) = 
 <a href="extpro_1.html#K4" title="EXTPRO_1:func.4">Following</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p3">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T3" title="EXTPRO_1:th.3">EXTPRO_1:3</a></span>
<br/>.= 
 <a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p1">(<span class="default"><a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p5">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span>)</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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span>)</span>)</span>)

;<br/>
<span class="kw">set </span><font color="Maroon" title="c20">s3</font> =  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p3">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>);<br/>
<span class="kw">set </span><font color="Maroon" title="c21">p3</font> = <font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>;<br/>
<span class="kw">assume </span><a NAME="E7:84_1"/><span class="lab"><font color="Green" title="E67">A10</font></span>: 
<font color="Maroon" title="c14">ss</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">a</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">ss</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">a</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 &amp; <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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp;  ex <font color="Olive" title="b1">k</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <br/>(  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<font color="Olive" title="b1">k</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span> &amp; (  for <font color="Olive" title="b2">n</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Olive" title="b2">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b1">k</font> holds <br/> <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<font color="Olive" title="b2">n</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> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span> ) ) )</span><br/>

<a NAME="E8:84_1"/><span class="lab"><font color="Green" title="E68">A11</font></span>: 
( <font color="Maroon" title="c11">I1</font> <a href="scm_halt.html#R1" title="SCM_HALT:pred.1">is_closed_onInit</a> <font color="Maroon" title="c14">ss</font>,<font color="Maroon" title="c15">pp</font> &amp; <font color="Maroon" title="c11">I1</font> <a href="scm_halt.html#R2" title="SCM_HALT:pred.2">is_halting_onInit</a> <font color="Maroon" title="c14">ss</font>,<font color="Maroon" title="c15">pp</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scm_halt.html#T25" target="_self" title="SCM_HALT:th.25">Th35</a>, <a class="ref" href="scm_halt.html#T26" target="_self" title="SCM_HALT:th.26">Th36</a></span>;<br/>
<a NAME="E9:84_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E69">A12</font></span>: 
 <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>) <a href="scm_halt.html#R2" title="SCM_HALT:pred.2">is_halting_onInit</a> <font color="Maroon" title="c14">ss</font>,<font color="Maroon" title="c15">pp</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:84_1"><span class="lab"><font color="Green" title="E67">A10</font></span></a>, <a class="ref" href="scm_halt.html#T35" target="_self" title="SCM_HALT:th.35">Th45</a></span>;<br/>
<a NAME="E10:84_1"/>
 <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>) <a href="scm_halt.html#R1" title="SCM_HALT:pred.1">is_closed_onInit</a> <font color="Maroon" title="c14">ss</font>,<font color="Maroon" title="c15">pp</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:84_1"><span class="lab"><font color="Green" title="E67">A10</font></span></a>, <a class="txt" href="#E8:84_1"><span class="lab"><font color="Green" title="E68">A11</font></span></a>, <a class="ref" href="scm_halt.html#T35" target="_self" title="SCM_HALT:th.35">Th45</a></span>;<br/>
<a NAME="E11:84_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E70">A13</font></span>: 
 <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p3">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>) <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p1">(<span class="default"><a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span>)</span>)</span>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:84_1"><span class="lab"><font color="Green" title="E69">A12</font></span></a>, <a class="txt" href="#E6:84_1"><span class="lab"><font color="Green" title="E66">A9</font></span></a>, <a class="ref" href="scm_halt.html#T59" target="_self" title="SCM_HALT:th.59">Th71</a></span>;<br/>
<a NAME="E12:84_1"/><span class="lab"><font color="Green" title="E71">A14</font></span>: 
 <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>) <a href="scm_halt.html#R1" title="SCM_HALT:pred.1">is_closed_onInit</a> <font color="Maroon" title="c14">ss</font>,<font color="Maroon" title="c15">pp</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:84_1"><span class="lab"><font color="Green" title="E67">A10</font></span></a>, <a class="txt" href="#E8:84_1"><span class="lab"><font color="Green" title="E68">A11</font></span></a>, <a class="ref" href="scm_halt.html#T35" target="_self" title="SCM_HALT:th.35">Th45</a></span>;<br/>
<span class="lab"><font color="Green" title="E72">A15</font></span>:  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c11">I1</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa8b.html#T11" title="SCMFSA8B:th.11">SCMFSA8B:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c11">I1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa8a.html#T15" title="SCMFSA8A:th.15">SCMFSA8A:15</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c11">I1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2

;<br/>
<span class="lab"><font color="Green" title="E73">A16</font></span>:  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span> = 
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p3">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#T62" title="CARD_1:th.62">CARD_1:62</a></span>
<br/>.= 
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T99" title="FUNCT_4:th.99">FUNCT_4:99</a></span>
<br/>.= 
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#T62" title="CARD_1:th.62">CARD_1:62</a></span>
;<br/>
<div><span class="lab"><font color="Green" title="E74">A17</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="84_1_5"><span class="kw">now </span></a><div class="add"><a NAME="E1:84_1_5"/><span class="lab"><font color="Green" title="E75">A18</font></span>: 
<font color="Maroon" title="c11">I1</font> <a href="scm_halt.html#R2" title="SCM_HALT:pred.2">is_halting_onInit</a> <font color="Maroon" title="c14">ss</font>,<font color="Maroon" title="c15">pp</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scm_halt.html#T26" target="_self" title="SCM_HALT:th.26">Th36</a></span>;<br/><a NAME="E2:84_1_5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E76">A19</font></span>: 
<font color="Maroon" title="c11">I1</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a>  <a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font>,<font color="Maroon" title="c15">pp</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scm_halt.html#T31" target="_self" title="SCM_HALT:th.31">Th41</a></span>;<br/><a NAME="E3:84_1_5"/>
<font color="Maroon" title="c11">I1</font> <a href="scm_halt.html#R1" title="SCM_HALT:pred.1">is_closed_onInit</a> <font color="Maroon" title="c14">ss</font>,<font color="Maroon" title="c15">pp</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scm_halt.html#T25" target="_self" title="SCM_HALT:th.25">Th35</a></span>;<br/><a NAME="E4:84_1_5"/><span class="kw">then </span>
 <a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span>,<font color="Maroon" title="c15">pp</font>,<font color="Maroon" title="c14">ss</font>) <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<font color="Maroon" title="c11">I1</font>,<font color="Maroon" title="c15">pp</font>,<font color="Maroon" title="c14">ss</font>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c11">I1</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span>,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:84_1"><span class="lab"><font color="Green" title="E67">A10</font></span></a>, <a class="txt" href="#E1:84_1_5"><span class="lab"><font color="Green" title="E75">A18</font></span></a>, <a class="ref" href="scm_halt.html#T36" target="_self" title="SCM_HALT:th.36">Th46</a></span>;<br/><a NAME="E5:84_1_5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E77">A20</font></span>: 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span>,<font color="Maroon" title="c15">pp</font>,<font color="Maroon" title="c14">ss</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<font color="Maroon" title="c11">I1</font>,<font color="Maroon" title="c15">pp</font>,<font color="Maroon" title="c14">ss</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_3.html#T3" title="SCMFSA_3:th.3">SCMFSA_3:3</a></span>;<br/><div><span class="kw">hereby </span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font> &amp; <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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">ss</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">a</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 &amp; <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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )</span>
<div class="add"><span class="kw">thus </span><a NAME="E1:84_1_5_1"/>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:84_1"><span class="lab"><font color="Green" title="E73">A16</font></span></a>, <a class="txt" href="#E13:84_1"><span class="lab"><font color="Green" title="E72">A15</font></span></a>, <a class="ref" href="afinsq_1.html#T66" title="AFINSQ_1:th.66">AFINSQ_1:66</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c11">I1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span><br/><a NAME="E2:84_1_5_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c11">I1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c11">I1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 ;<br/><a NAME="E3:84_1_5_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c11">I1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:84_1"><span class="lab"><font color="Green" title="E72">A15</font></span></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/><a NAME="E4:84_1_5_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c11">I1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:84_1"><span class="lab"><font color="Green" title="E73">A16</font></span></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/><span class="kw">hence </span><a NAME="E5:84_1_5_1"/>
<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c11">I1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T66" title="AFINSQ_1:th.66">AFINSQ_1:66</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><span class="kw">consider </span><font color="Maroon" title="c22">Is</font> being   <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a><span class="kw"> such that </span><br/><a NAME="E8:84_1_5"/><span class="lab"><font color="Green" title="E78">A21</font></span>: 
<font color="Maroon" title="c22">Is</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>
 ;<br/><span class="lab"><font color="Green" title="E79">A22</font></span>: <font color="Maroon" title="c22">Is</font> = 
<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmfsa_3.html#K1" title="SCMFSA_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:84_1_5"><span class="lab"><font color="Green" title="E78">A21</font></span></a>, <a class="ref" href="funct_4.html#T93" title="FUNCT_4:th.93">FUNCT_4:93</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmfsa_3.html#K1" title="SCMFSA_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></span>
<br/>.= 
 <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T93" title="FUNCT_4:th.93">FUNCT_4:93</a></span>
;<br/><a NAME="E10:84_1_5"/>
<font color="Maroon" title="c11">I1</font> <a href="scm_halt.html#R1" title="SCM_HALT:pred.1">is_closed_onInit</a> <font color="Maroon" title="c14">ss</font>,<font color="Maroon" title="c15">pp</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scm_halt.html#T25" target="_self" title="SCM_HALT:th.25">Th35</a></span>;<br/><a NAME="E11:84_1_5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E80">A23</font></span>: 
<font color="Maroon" title="c11">I1</font> <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a>  <a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font>,<font color="Maroon" title="c15">pp</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scm_halt.html#T30" target="_self" title="SCM_HALT:th.30">Th40</a></span>;<br/><a NAME="E12:84_1_5"/>
<font color="Maroon" title="c11">I1</font> <a href="scm_halt.html#R2" title="SCM_HALT:pred.2">is_halting_onInit</a> <font color="Maroon" title="c14">ss</font>,<font color="Maroon" title="c15">pp</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scm_halt.html#T26" target="_self" title="SCM_HALT:th.26">Th36</a></span>;<br/><a NAME="E13:84_1_5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E81">A24</font></span>: 
<font color="Maroon" title="c11">I1</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a>  <a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font>,<font color="Maroon" title="c15">pp</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scm_halt.html#T31" target="_self" title="SCM_HALT:th.31">Th41</a></span>;<br/><a NAME="E14:84_1_5"/><span class="lab"><font color="Green" title="E82">A25</font></span>: 
<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">a</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:84_1"><span class="lab"><font color="Green" title="E67">A10</font></span></a>, <a class="ref" href="scmfsa6c.html#T3" title="SCMFSA6C:th.3">SCMFSA6C:3</a></span>;<br/><a NAME="E15:84_1_5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E83">A26</font></span>: 
 <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>) <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a>  <a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font>,<font color="Maroon" title="c15">pp</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:84_1_5"><span class="lab"><font color="Green" title="E80">A23</font></span></a>, <a class="txt" href="#E13:84_1_5"><span class="lab"><font color="Green" title="E81">A24</font></span></a>, <a class="ref" href="scmfsa8b.html#T15" title="SCMFSA8B:th.15">SCMFSA8B:15</a></span>;<br/><span class="kw">thus </span><a NAME="E16:84_1_5"/>
 <a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">ss</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">a</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 &amp; <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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )</span><br/><div><span class="lab"><font color="Green" title="E84">A28</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="84_1_5_3"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c23">b</font> be    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c23">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<font color="Maroon" title="c22">Is</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<font color="Maroon" title="c22">Is</font>)</span>)</span>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c23">b</font></span><br/><a NAME="E1:84_1_5_3"/>
<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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c23">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c23">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:84_1"><span class="lab"><font color="Green" title="E70">A13</font></span></a>, <a class="ref" href="scmfsa_2.html#T69" title="SCMFSA_2:th.69">SCMFSA_2:69</a></span>;<br/><span class="kw">hence </span><a NAME="E2:84_1_5_3"/>
<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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c23">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<font color="Maroon" title="c22">Is</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<font color="Maroon" title="c22">Is</font>)</span>)</span>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c23">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:84_1_5"><span class="lab"><font color="Green" title="E78">A21</font></span></a>, <a class="txt" href="#E9:84_1"><span class="lab"><font color="Green" title="E69">A12</font></span></a>, <a class="txt" href="#E12:84_1"><span class="lab"><font color="Green" title="E71">A14</font></span></a>, <a class="ref" href="scm_halt.html#T57" target="_self" title="SCM_HALT:th.57">Th68</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><span class="kw">then </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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">a</font> = 
<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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<font color="Maroon" title="c22">Is</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<font color="Maroon" title="c22">Is</font>)</span>)</span>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">a</font>

<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span>,<font color="Maroon" title="c15">pp</font>,<font color="Maroon" title="c14">ss</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">a</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:84_1_5"><span class="lab"><font color="Green" title="E83">A26</font></span></a>, <a class="txt" href="#E9:84_1_5"><span class="lab"><font color="Green" title="E79">A22</font></span></a>, <a class="ref" href="scmfsa8c.html#T58" title="SCMFSA8C:th.58">SCMFSA8C:58</a></span>
;<br/><span class="kw">hence </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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">a</font> = 
<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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">I1</font></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c11">I1</font></span>)</span>,<span class="p3">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span></span>)</span>)</span>)</span>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">a</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:84_1_5"><span class="lab"><font color="Green" title="E76">A19</font></span></a>, <a class="txt" href="#E5:84_1_5"><span class="lab"><font color="Green" title="E77">A20</font></span></a>, <a class="ref" href="scmfsa8c.html#T58" title="SCMFSA8C:th.58">SCMFSA8C:58</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c14">ss</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">a</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:84"><span class="lab"><font color="Green" title="E60">A1</font></span></a>, <a class="ref" href="scm_halt.html#T54" target="_self" title="SCM_HALT:th.54">Th64</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1</span><br/><a NAME="E20:84_1_5"/><span class="lab"><font color="Green" title="E85">A29</font></span>: 
 <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>) <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a>  <a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font>,<font color="Maroon" title="c15">pp</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:84_1_5"><span class="lab"><font color="Green" title="E82">A25</font></span></a>, <a class="txt" href="#E11:84_1_5"><span class="lab"><font color="Green" title="E80">A23</font></span></a>, <a class="txt" href="#E13:84_1_5"><span class="lab"><font color="Green" title="E81">A24</font></span></a>, <a class="ref" href="scmfsa8b.html#T15" title="SCMFSA8B:th.15">SCMFSA8B:15</a></span>;<br/><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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<font color="Maroon" title="c22">Is</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<font color="Maroon" title="c22">Is</font>)</span>)</span>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:84_1_5"><span class="lab"><font color="Green" title="E84">A28</font></span></a></span>
<br/>.= 
1
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:84_1_5"><span class="lab"><font color="Green" title="E83">A26</font></span></a>, <a class="txt" href="#E20:84_1_5"><span class="lab"><font color="Green" title="E85">A29</font></span></a>, <a class="txt" href="#E9:84_1_5"><span class="lab"><font color="Green" title="E79">A22</font></span></a>, <a class="ref" href="scmfsa8c.html#T67" title="SCMFSA8C:th.67">SCMFSA8C:67</a></span>
;<br/><span class="kw">hence </span><a NAME="E22:84_1_5"/>
<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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ; <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">hence </span><a NAME="E16:84_1"/>
( <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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">ss</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">a</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 &amp; <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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 ; <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#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <br/>(  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<font color="Olive" title="b1">k</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span> &amp; (  for <font color="Olive" title="b2">n</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Olive" title="b2">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b1">k</font> holds <br/> <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<font color="Olive" title="b2">n</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> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span> ) )</span><br/>

<a NAME="E17:84_1"/><span class="lab"><font color="Green" title="E75">A30</font></span>: 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <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="#E11:84_1"><span class="lab"><font color="Green" title="E70">A13</font></span></a>, <a class="ref" href="scmfsa_2.html#T69" title="SCMFSA_2:th.69">SCMFSA_2:69</a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="84_1_6"><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="E1:84_1_6"/>
( <font color="Maroon" title="c13">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <font color="Maroon" title="c13">k</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="84_1_6_1"><span class="kw">suppose </span></a><a NAME="E1:84_1_6_1"/><span class="lab"><font color="Green" title="E76">A31</font></span>: 
<font color="Maroon" title="c13">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <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#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <br/>(  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<font color="Olive" title="b1">k</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span> &amp; (  for <font color="Olive" title="b2">n</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Olive" title="b2">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b1">k</font> holds <br/> <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<font color="Olive" title="b2">n</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> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span> ) )</span><br/><div class="add"><span class="kw">take </span><font color="Maroon" title="c22">m</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<font color="Maroon" title="c22">m</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span> &amp; (  for <font color="Olive" title="b1">n</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Olive" title="b1">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c22">m</font> holds <br/> <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<font color="Olive" title="b1">n</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> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span> ) )</span><br/><span class="lab"><font color="Green" title="E77">A32</font></span>:  <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p3">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span>) = 
<span class="p1">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p3">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:84_1"><span class="lab"><font color="Green" title="E75">A30</font></span></a>, <a class="ref" href="pboole.html#T143" title="PBOOLE:th.143">PBOOLE:143</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.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="#E15:84_1"><span class="lab"><font color="Green" title="E74">A17</font></span></a>, <a class="txt" href="#E4:84_1"><span class="lab"><font color="Green" title="E64">A7</font></span></a>, <a class="ref" href="grfunc_1.html#T2" title="GRFUNC_1:th.2">GRFUNC_1:2</a></span>
<br/>.= 
<font color="Maroon" title="c9">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c11">I1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:84_1"><span class="lab"><font color="Green" title="E62">A3</font></span></a>, <a class="ref" href="funct_4.html#T105" title="FUNCT_4:th.105">FUNCT_4:105</a></span>
;<br/><span class="lab"><font color="Green" title="E78">A33</font></span>:  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p3">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>) = 
 <a href="extpro_1.html#K4" title="EXTPRO_1:func.4">Following</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p3">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T3" title="EXTPRO_1:th.3">EXTPRO_1:3</a></span>
<br/>.= 
 <a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c9">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c11">I1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:84_1_6_1"><span class="lab"><font color="Green" title="E77">A32</font></span></a></span>
;<br/><a NAME="E4:84_1_6_1"/><span class="kw">then </span>
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c11">I1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:84_1"><span class="lab"><font color="Green" title="E65">A8</font></span></a>, <a class="txt" href="#E15:84_1"><span class="lab"><font color="Green" title="E74">A17</font></span></a>, <a class="txt" href="#E1:84_1_6_1"><span class="lab"><font color="Green" title="E76">A31</font></span></a>, <a class="ref" href="scmfsa_2.html#T70" title="SCMFSA_2:th.70">SCMFSA_2:70</a></span>;<br/><span class="kw">then </span><span class="lab"><font color="Green" title="E79">A34</font></span>:  <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p3">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span>) = 
<span class="p1">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p3">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c11">I1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#T143" title="PBOOLE:th.143">PBOOLE:143</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c11">I1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:84_1"><span class="lab"><font color="Green" title="E74">A17</font></span></a>, <a class="txt" href="#E4:84_1"><span class="lab"><font color="Green" title="E64">A7</font></span></a>, <a class="ref" href="grfunc_1.html#T2" title="GRFUNC_1:th.2">GRFUNC_1:2</a></span>
<br/>.= 
 <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p2">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p3">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:84_1"><span class="lab"><font color="Green" title="E62">A3</font></span></a>, <a class="ref" href="funct_4.html#T105" title="FUNCT_4:th.105">FUNCT_4:105</a></span>
;<br/> <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p3">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<font color="Maroon" title="c22">m</font>) = 
 <a href="extpro_1.html#K4" title="EXTPRO_1:func.4">Following</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p3">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T3" title="EXTPRO_1:th.3">EXTPRO_1:3</a></span>
<br/>.= 
 <a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p1">(<span class="default"><a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:84_1_6_1"><span class="lab"><font color="Green" title="E79">A34</font></span></a></span>
;<br/><span class="kw">hence </span><a NAME="E7:84_1_6_1"/>
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<font color="Maroon" title="c22">m</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T69" title="SCMFSA_2:th.69">SCMFSA_2:69</a></span>; <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">n</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Olive" title="b1">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c22">m</font> holds <br/> <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<font color="Olive" title="b1">n</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> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span><br/><div><span class="kw">hereby </span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span>
<div class="add"><span class="kw">let </span><font color="Maroon" title="c23">n</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">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"> ( <font color="Maroon" title="c23">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c22">m</font> implies  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<font color="Olive">b<sub>1</sub></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> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span> )</span><br/><span class="kw">assume </span><a NAME="E1:84_1_6_1_5"/>
<font color="Maroon" title="c23">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c22">m</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<font color="Olive">b<sub>1</sub></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> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span><br/><a NAME="E2:84_1_6_1_5"/><span class="kw">then </span>
<font color="Maroon" title="c23">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/><a NAME="E3:84_1_6_1_5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E80">A35</font></span>: 
( <font color="Maroon" title="c23">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 or <font color="Maroon" title="c23">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T8" title="NAT_1:th.8">NAT_1:8</a></span>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="84_1_6_1_5_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="E1:84_1_6_1_5_1"/>
( <font color="Maroon" title="c23">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>) or <font color="Maroon" title="c23">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 or <font color="Maroon" title="c23">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:84_1_6_1_5"><span class="lab"><font color="Green" title="E80">A35</font></span></a>, <a class="ref" href="nat_1.html#T8" title="NAT_1:th.8">NAT_1:8</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="84_1_6_1_5_1_1"><span class="kw">suppose </span></a><a NAME="E1:84_1_6_1_5_1_1"/><span class="lab"><font color="Green" title="E81">A36</font></span>: 
<font color="Maroon" title="c23">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<font color="Olive">b<sub>1</sub></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> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span><br/><div class="add"><a NAME="E2:84_1_6_1_5_1_1"/><span class="lab"><font color="Green" title="E82">A37</font></span>: 
( <font color="Maroon" title="c11">I1</font> <a href="scm_halt.html#R1" title="SCM_HALT:pred.1">is_closed_onInit</a> <font color="Maroon" title="c14">ss</font>,<font color="Maroon" title="c15">pp</font> &amp; <font color="Maroon" title="c11">I1</font> <a href="scm_halt.html#R2" title="SCM_HALT:pred.2">is_halting_onInit</a> <font color="Maroon" title="c14">ss</font>,<font color="Maroon" title="c15">pp</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scm_halt.html#T25" target="_self" title="SCM_HALT:th.25">Th35</a>, <a class="ref" href="scm_halt.html#T26" target="_self" title="SCM_HALT:th.26">Th36</a></span>;<br/><a NAME="E3:84_1_6_1_5_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E83">A38</font></span>: 
 <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>) <a href="scm_halt.html#R1" title="SCM_HALT:pred.1">is_closed_onInit</a> <font color="Maroon" title="c14">ss</font>,<font color="Maroon" title="c15">pp</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:84_1"><span class="lab"><font color="Green" title="E67">A10</font></span></a>, <a class="ref" href="scm_halt.html#T35" target="_self" title="SCM_HALT:th.35">Th45</a></span>;<br/><a NAME="E4:84_1_6_1_5_1_1"/>
 <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>) <a href="scm_halt.html#R2" title="SCM_HALT:pred.2">is_halting_onInit</a> <font color="Maroon" title="c14">ss</font>,<font color="Maroon" title="c15">pp</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:84_1"><span class="lab"><font color="Green" title="E67">A10</font></span></a>, <a class="txt" href="#E2:84_1_6_1_5_1_1"><span class="lab"><font color="Green" title="E82">A37</font></span></a>, <a class="ref" href="scm_halt.html#T35" target="_self" title="SCM_HALT:th.35">Th45</a></span>;<br/><a NAME="E5:84_1_6_1_5_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E84">A39</font></span>: 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<font color="Maroon" title="c23">n</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<font color="Maroon" title="c23">n</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:84_1_6_1_5_1_1"><span class="lab"><font color="Green" title="E81">A36</font></span></a>, <a class="txt" href="#E3:84_1_6_1_5_1_1"><span class="lab"><font color="Green" title="E83">A38</font></span></a>, <a class="ref" href="scm_halt.html#T57" target="_self" title="SCM_HALT:th.57">Th68</a></span>;<br/><a NAME="E6:84_1_6_1_5_1_1"/>
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<font color="Maroon" title="c23">n</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> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:84_1_6_1_5_1_1"><span class="lab"><font color="Green" title="E83">A38</font></span></a>, <a class="ref" href="scm_halt.html#D4" target="_self" title="SCM_HALT:def.4">Def4</a></span>;<br/><span class="kw">hence </span><a NAME="E7:84_1_6_1_5_1_1"/>
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<font color="Maroon" title="c23">n</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> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:84_1_6_1_5_1_1"><span class="lab"><font color="Green" title="E84">A39</font></span></a>, <a class="ref" href="funct_4.html#T99" title="FUNCT_4:th.99">FUNCT_4:99</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="84_1_6_1_5_1_2"><span class="kw">suppose </span></a><a NAME="E1:84_1_6_1_5_1_2"/>
<font color="Maroon" title="c23">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<font color="Olive">b<sub>1</sub></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> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:84_1_6_1_5_1_2"/>
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<font color="Maroon" title="c23">n</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> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:84_1"><span class="lab"><font color="Green" title="E70">A13</font></span></a>, <a class="txt" href="#E15:84_1"><span class="lab"><font color="Green" title="E74">A17</font></span></a>, <a class="ref" href="scmfsa_2.html#T69" title="SCMFSA_2:th.69">SCMFSA_2:69</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="84_1_6_1_5_1_3"><span class="kw">suppose </span></a><a NAME="E1:84_1_6_1_5_1_3"/>
<font color="Maroon" title="c23">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<font color="Olive">b<sub>1</sub></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> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:84_1_6_1_5_1_3"/>
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<font color="Maroon" title="c23">n</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> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:84_1"><span class="lab"><font color="Green" title="E65">A8</font></span></a>, <a class="txt" href="#E15:84_1"><span class="lab"><font color="Green" title="E74">A17</font></span></a>, <a class="txt" href="#E1:84_1_6_1"><span class="lab"><font color="Green" title="E76">A31</font></span></a>, <a class="txt" href="#E3:84_1_6_1"><span class="lab"><font color="Green" title="E78">A33</font></span></a>, <a class="ref" href="scmfsa_2.html#T70" title="SCMFSA_2:th.70">SCMFSA_2:70</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></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="84_1_6_2"><span class="kw">suppose </span></a><a NAME="E1:84_1_6_2"/><span class="lab"><font color="Green" title="E76">A40</font></span>: 
<font color="Maroon" title="c13">k</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <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#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <br/>(  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<font color="Olive" title="b1">k</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span> &amp; (  for <font color="Olive" title="b2">n</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Olive" title="b2">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b1">k</font> holds <br/> <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<font color="Olive" title="b2">n</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> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span> ) )</span><br/><div class="add"><span class="kw">consider </span><font color="Maroon" title="c22">Is3</font> being   <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a><span class="kw"> such that </span><br/><a NAME="E3:84_1_6_2"/><span class="lab"><font color="Green" title="E77">A41</font></span>: 
<font color="Maroon" title="c22">Is3</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span>
 ;<br/><span class="kw">consider </span><font color="Maroon" title="c23">m0</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <span class="kw"> such that </span><br/><a NAME="E5:84_1_6_2"/><span class="lab"><font color="Green" title="E78">A44</font></span>: 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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"><span class="p3">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p5">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c22">Is3</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmfsa_3.html#K1" title="SCMFSA_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c23">m0</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>
 <span class="kw">and </span><br/><a NAME="E6:84_1_6_2"/><span class="lab"><font color="Green" title="E79">A45</font></span>: 
 for <font color="Olive" title="b1">n</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Olive" title="b1">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c23">m0</font> holds <br/> <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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"><span class="p3">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p5">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c22">Is3</font></span>)</span>,<font color="Olive" title="b1">n</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> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:84_1"><span class="lab"><font color="Green" title="E63">A6</font></span></a>, <a class="txt" href="#E1:84_1_6_2"><span class="lab"><font color="Green" title="E76">A40</font></span></a>, <a class="txt" href="#E5:84_1"><span class="lab"><font color="Green" title="E65">A8</font></span></a>, <a class="txt" href="#E15:84_1"><span class="lab"><font color="Green" title="E74">A17</font></span></a>, <a class="txt" href="#E3:84_1_6_2"><span class="lab"><font color="Green" title="E77">A41</font></span></a></span>;<br/><span class="kw">take </span><font color="Maroon" title="c24">m</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c23">m0</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<font color="Maroon" title="c24">m</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span> &amp; (  for <font color="Olive" title="b1">n</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Olive" title="b1">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c24">m</font> holds <br/> <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<font color="Olive" title="b1">n</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> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span> ) )</span><br/><a NAME="E7:84_1_6_2"/><span class="lab"><font color="Green" title="E80">A46</font></span>: 
 <a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p5">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p3">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:84_1"><span class="lab"><font color="Green" title="E75">A30</font></span></a>, <a class="txt" href="#E15:84_1"><span class="lab"><font color="Green" title="E74">A17</font></span></a>, <a class="ref" href="scmfsa6a.html#T37" title="SCMFSA6A:th.37">SCMFSA6A:37</a></span>;<br/><a NAME="E8:84_1_6_2"/><span class="lab"><font color="Green" title="E81">A47</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p3">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T25" title="FUNCT_4:th.25">FUNCT_4:25</a>, <a class="ref" href="funct_4.html#T98" title="FUNCT_4:th.98">FUNCT_4:98</a></span>;<br/><span class="kw">hence </span><a NAME="E9:84_1_6_2"/>
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<font color="Maroon" title="c24">m</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:84_1_6_2"><span class="lab"><font color="Green" title="E77">A41</font></span></a>, <a class="txt" href="#E5:84_1_6_2"><span class="lab"><font color="Green" title="E78">A44</font></span></a>, <a class="txt" href="#E7:84_1_6_2"><span class="lab"><font color="Green" title="E80">A46</font></span></a>, <a class="ref" href="extpro_1.html#T4" title="EXTPRO_1:th.4">EXTPRO_1:4</a></span>; <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">n</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Olive" title="b1">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c24">m</font> holds <br/> <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<font color="Olive" title="b1">n</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> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span><br/><div><span class="kw">hereby </span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span>
<div class="add"><span class="kw">let </span><font color="Maroon" title="c25">n</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">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"> ( <font color="Maroon" title="c25">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c24">m</font> implies  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<font color="Olive">b<sub>1</sub></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> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span> )</span><br/><span class="kw">assume </span><a NAME="E1:84_1_6_2_1"/><span class="lab"><font color="Green" title="E82">A48</font></span>: 
<font color="Maroon" title="c25">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c24">m</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<font color="Olive">b<sub>1</sub></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> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span><br/><a NAME="E2:84_1_6_2_1"/><span class="lab"><font color="Green" title="E83">A49</font></span>: 
( <font color="Maroon" title="c11">I1</font> <a href="scm_halt.html#R1" title="SCM_HALT:pred.1">is_closed_onInit</a> <font color="Maroon" title="c14">ss</font>,<font color="Maroon" title="c15">pp</font> &amp; <font color="Maroon" title="c11">I1</font> <a href="scm_halt.html#R2" title="SCM_HALT:pred.2">is_halting_onInit</a> <font color="Maroon" title="c14">ss</font>,<font color="Maroon" title="c15">pp</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scm_halt.html#T25" target="_self" title="SCM_HALT:th.25">Th35</a>, <a class="ref" href="scm_halt.html#T26" target="_self" title="SCM_HALT:th.26">Th36</a></span>;<br/><a NAME="E3:84_1_6_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E84">A50</font></span>: 
 <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>) <a href="scm_halt.html#R1" title="SCM_HALT:pred.1">is_closed_onInit</a> <font color="Maroon" title="c14">ss</font>,<font color="Maroon" title="c15">pp</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:84_1"><span class="lab"><font color="Green" title="E67">A10</font></span></a>, <a class="ref" href="scm_halt.html#T35" target="_self" title="SCM_HALT:th.35">Th45</a></span>;<br/><a NAME="E4:84_1_6_2_1"/><span class="lab"><font color="Green" title="E85">A51</font></span>: 
 <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>) <a href="scm_halt.html#R2" title="SCM_HALT:pred.2">is_halting_onInit</a> <font color="Maroon" title="c14">ss</font>,<font color="Maroon" title="c15">pp</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:84_1"><span class="lab"><font color="Green" title="E67">A10</font></span></a>, <a class="txt" href="#E2:84_1_6_2_1"><span class="lab"><font color="Green" title="E83">A49</font></span></a>, <a class="ref" href="scm_halt.html#T35" target="_self" title="SCM_HALT:th.35">Th45</a></span>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="84_1_6_2_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="E1:84_1_6_2_1_1"/>
( <font color="Maroon" title="c25">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>) or <span class="p1">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c25">n</font> )
 </span><span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="84_1_6_2_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:84_1_6_2_1_1_1"/>
<font color="Maroon" title="c25">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<font color="Olive">b<sub>1</sub></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> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span><br/><div class="add"><a NAME="E2:84_1_6_2_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E86">A52</font></span>: 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<font color="Maroon" title="c25">n</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<font color="Maroon" title="c25">n</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:84_1_6_2_1"><span class="lab"><font color="Green" title="E84">A50</font></span></a>, <a class="txt" href="#E4:84_1_6_2_1"><span class="lab"><font color="Green" title="E85">A51</font></span></a>, <a class="ref" href="scm_halt.html#T57" target="_self" title="SCM_HALT:th.57">Th68</a></span>;<br/><a NAME="E3:84_1_6_2_1_1_1"/>
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<font color="Maroon" title="c25">n</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> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:84_1_6_2_1"><span class="lab"><font color="Green" title="E84">A50</font></span></a>, <a class="ref" href="scm_halt.html#D4" target="_self" title="SCM_HALT:def.4">Def4</a></span>;<br/><span class="kw">hence </span><a NAME="E4:84_1_6_2_1_1_1"/>
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<font color="Maroon" title="c25">n</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> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:84_1_6_2_1_1_1"><span class="lab"><font color="Green" title="E86">A52</font></span></a>, <a class="ref" href="funct_4.html#T99" title="FUNCT_4:th.99">FUNCT_4:99</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="84_1_6_2_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:84_1_6_2_1_1_2"/><span class="lab"><font color="Green" title="E86">A53</font></span>: 
<span class="p1">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c25">n</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<font color="Olive">b<sub>1</sub></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> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span><br/><div class="add"><span class="kw">consider </span><font color="Maroon" title="c26">mm</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <span class="kw"> such that </span><br/><a NAME="E3:84_1_6_2_1_1_2"/><span class="lab"><font color="Green" title="E87">A54</font></span>: 
<font color="Maroon" title="c26">mm</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c25">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 ;<br/><a NAME="E4:84_1_6_2_1_1_2"/>
<font color="Maroon" title="c25">n</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:84_1_6_2_1_1_2"><span class="lab"><font color="Green" title="E86">A53</font></span></a>, <a class="ref" href="xreal_1.html#T48" title="XREAL_1:th.48">XREAL_1:48</a></span>;<br/><a NAME="E5:84_1_6_2_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E88">A55</font></span>: 
<font color="Maroon" title="c26">mm</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c25">n</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:84_1_6_2_1_1_2"><span class="lab"><font color="Green" title="E87">A54</font></span></a>, <a class="ref" href="xreal_0.html#D2" title="XREAL_0:def.2">XREAL_0:def 2</a></span>;<br/><a NAME="E6:84_1_6_2_1_1_2"/>
<font color="Maroon" title="c26">mm</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c25">n</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:84_1_6_2_1_1_2"><span class="lab"><font color="Green" title="E86">A53</font></span></a>, <a class="txt" href="#E3:84_1_6_2_1_1_2"><span class="lab"><font color="Green" title="E87">A54</font></span></a>, <a class="ref" href="xreal_1.html#T235" title="XREAL_1:th.235">XREAL_1:235</a></span>;<br/><a NAME="E7:84_1_6_2_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E89">A56</font></span>: 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<font color="Maroon" title="c25">n</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p5">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p0">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p0">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span>,<font color="Maroon" title="c26">mm</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T4" title="EXTPRO_1:th.4">EXTPRO_1:4</a></span>;<br/><a NAME="E8:84_1_6_2_1_1_2"/>
<font color="Maroon" title="c23">m0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">m</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 ;<br/><a NAME="E9:84_1_6_2_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c26">mm</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c23">m0</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:84_1_6_2_1"><span class="lab"><font color="Green" title="E82">A48</font></span></a>, <a class="txt" href="#E5:84_1_6_2_1_1_2"><span class="lab"><font color="Green" title="E88">A55</font></span></a>, <a class="ref" href="xreal_1.html#T9" title="XREAL_1:th.9">XREAL_1:9</a></span>;<br/><span class="kw">hence </span><a NAME="E10:84_1_6_2_1_1_2"/>
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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="c15">pp</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c14">ss</font></span>)</span>,<font color="Maroon" title="c25">n</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> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:84_1_6_2"><span class="lab"><font color="Green" title="E77">A41</font></span></a>, <a class="txt" href="#E6:84_1_6_2"><span class="lab"><font color="Green" title="E79">A45</font></span></a>, <a class="txt" href="#E7:84_1_6_2"><span class="lab"><font color="Green" title="E80">A46</font></span></a>, <a class="txt" href="#E8:84_1_6_2"><span class="lab"><font color="Green" title="E81">A47</font></span></a>, <a class="txt" href="#E7:84_1_6_2_1_1_2"><span class="lab"><font color="Green" title="E89">A56</font></span></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></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E4:84"/><span class="lab"><font color="Green" title="E62">A57</font></span>: 
<font color="Maroon" title="c6">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ; <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="c6">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">a</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or  <a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span> <a href="scmfsa8a.html#R1" title="SCMFSA8A:pred.1">is_pseudo-closed_on</a> <font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c7">p</font> )</span><br/>

<span class="kw">assume </span><a NAME="E5:84"/><span class="lab"><font color="Green" title="E63">A58</font></span>: 
<font color="Maroon" title="c6">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">a</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span> <a href="scmfsa8a.html#R1" title="SCMFSA8A:pred.1">is_pseudo-closed_on</a> <font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c7">p</font></span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c13">sa</font> = <font color="Maroon" title="c6">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c9">a</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">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="int_1.html#T3" title="INT_1:th.3">INT_1:3</a></span>;<br/>
<a NAME="E7:84"/><span class="lab"><font color="Green" title="E64">A59</font></span>: 
<font color="Maroon">S<sub>1</sub></font>[ <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ]
 
;<br/>
<a NAME="E8:84"/>
 for <font color="Olive" title="b1">k</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font>]
 
<span class="kw">from</span> <span class="lab"><a class="ref" href="nat_1.html#S1" title="NAT_1:sch.1">NAT_1:sch 1</a>(<a class="txt" href="#E7:84"><span class="lab"><font color="Green" title="E64">A59</font></span></a>, <a class="txt" href="#E3:84"><span class="lab"><font color="Green" title="E61">A2</font></span></a>);<br/></span>
<a NAME="E9:84"/><span class="kw">then </span><span class="lab"><font color="Green" title="E65">B60</font></span>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c13">sa</font>]
 
;<br/>
<a NAME="E10:84"/><span class="lab"><font color="Green" title="E66">X4</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></span>;<br/>
<a NAME="E11:84"/>
 <a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T56" title="SCMFSA_2:th.56">SCMFSA_2:56</a></span>;<br/>
<a NAME="E12:84"/><span class="kw">then </span>
 not  <a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:84"><span class="lab"><font color="Green" title="E66">X4</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<a NAME="E13:84"/><span class="kw">then </span><span class="lab"><font color="Green" title="E67">X1</font></span>: 
<span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c6">s</font></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:84"><span class="lab"><font color="Green" title="E62">A57</font></span></a>, <a class="ref" href="funct_4.html#T11" title="FUNCT_4:th.11">FUNCT_4:11</a></span>;<br/>
<a NAME="E14:84"/>
 <a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:84"><span class="lab"><font color="Green" title="E66">X4</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E68">X2</font></span>:  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c6">s</font></span>)</span> = 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T13" title="FUNCT_4:th.13">FUNCT_4:13</a></span>
<br/>.= 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T72" title="FUNCOP_1:th.72">FUNCOP_1:72</a></span>
;<br/>
<a NAME="E16:84"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmfsa_3.html#K1" title="SCMFSA_3:func.1">.--&gt;</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="sfmastr1.html#K1" title="SFMASTR1:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span></span><a href="sfmastr1.html#K1" title="SFMASTR1:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></span>;<br/>
<a NAME="E17:84"/><span class="kw">then </span><span class="lab"><font color="Green" title="E69">X3</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>)</span>)</span> <a href="subset_1.html#R1" title="SUBSET_1:pred.1">misses</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmfsa_3.html#K1" title="SCMFSA_3:func.1">.--&gt;</a> 1</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:84"><span class="lab"><font color="Green" title="E66">X4</font></span></a>, <a class="ref" href="scmfsa_2.html#T56" title="SCMFSA_2:th.56">SCMFSA_2:56</a>, <a class="ref" href="zfmisc_1.html#T11" title="ZFMISC_1:th.11">ZFMISC_1:11</a></span>;<br/>
 <a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c6">s</font> = 
<font color="Maroon" title="c6">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmfsa_3.html#K1" title="SCMFSA_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:84"><span class="lab"><font color="Green" title="E69">X3</font></span></a>, <a class="ref" href="funct_4.html#T35" title="FUNCT_4:th.35">FUNCT_4:35</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c6">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmfsa_3.html#K1" title="SCMFSA_3:func.1">.--&gt;</a> 1</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c6">s</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmfsa_3.html#K1" title="SCMFSA_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:84"><span class="lab"><font color="Green" title="E69">X3</font></span></a>, <a class="ref" href="funct_4.html#T115" title="FUNCT_4:th.115">FUNCT_4:115</a></span>
<br/>.= 
 <a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c6">s</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></span>
<br/>.= 
 <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c6">s</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:84"><span class="lab"><font color="Green" title="E67">X1</font></span></a>, <a class="txt" href="#E15:84"><span class="lab"><font color="Green" title="E68">X2</font></span></a>, <a class="ref" href="scmfsa6a.html#T37" title="SCMFSA6A:th.37">SCMFSA6A:37</a></span>
;<br/>
<a NAME="E19:84"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">k</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <br/>(  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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="c7">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c6">s</font></span>)</span>,<font color="Olive" title="b1">k</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span> &amp; (  for <font color="Olive" title="b2">n</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Olive" title="b2">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b1">k</font> holds <br/> <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">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="c7">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p4">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c6">s</font></span>)</span>,<font color="Olive" title="b2">n</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> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p3">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span> ) )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:84"><span class="lab"><font color="Green" title="E65">B60</font></span></a>, <a class="txt" href="#E4:84"><span class="lab"><font color="Green" title="E62">A57</font></span></a>, <a class="txt" href="#E5:84"><span class="lab"><font color="Green" title="E63">A58</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E20:84"/>
 <a href="scmfsa8c.html#K1" title="SCMFSA8C:func.1">loop</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c9">a</font>,<span class="p2">(<span class="default"><a href="scmfsa8a.html#K1" title="SCMFSA8A:func.1">Goto</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">I</font> <a href="scmfsa6a.html#K6" title="SCMFSA6A:func.6">';'</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c9">a</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>)</span>)</span></span>)</span>)</span>)</span> <a href="scmfsa8a.html#R1" title="SCMFSA8A:pred.1">is_pseudo-closed_on</a> <font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c7">p</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa8a.html#D2" title="SCMFSA8A:def.2">SCMFSA8A:def 2</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>
