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<span class="kw">let </span><font color="Maroon" title="c3">P</font> be   <a href="compos_1.html#NM2" title="COMPOS_1:NM.2">Instruction-Sequence</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">s</font> being   <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="memstr_0.html#V4" title="MEMSTR_0:attr.4">-started</a>  <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a><br/>  for <font color="Olive" title="b2">sp</font>, <font color="Olive" title="b3">cv</font>, <font color="Olive" title="b4">result</font>, <font color="Olive" title="b5">pp</font>, <font color="Olive" title="b6">pD</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> <br/>  for <font color="Olive" title="b7">f</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Olive" title="b1">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Olive" title="b2">sp</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Olive" title="b2">sp</font> &amp; <font color="Olive" title="b3">cv</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b4">result</font> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b1">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Olive" title="b2">sp</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b4">result</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b5">pp</font> &amp; <font color="Olive" title="b5">pp</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b6">pD</font> &amp; <font color="Olive" title="b6">pD</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b1">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Olive" title="b6">pD</font></span>)</span> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b7">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> (<span class="p2">(<span class="default"><font color="Olive" title="b1">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Olive" title="b2">sp</font></span>)</span></span>)</span>,<font color="Olive" title="b3">cv</font>)</span>)</span> &amp; (  for <font color="Olive" title="b8">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="Olive" title="b8">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b7">f</font> holds <br/><font color="Olive" title="b7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b8">k</font> <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="Olive" title="b1">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> (<span class="p2">(<span class="default"><font color="Olive" title="b1">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Olive" title="b6">pD</font></span>)</span></span>)</span>,<font color="Olive" title="b8">k</font>)</span>)</span> ) holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><a href="scmpds_7.html#K4" title="SCMPDS_7:func.4">sum</a> (<font color="Olive" title="b2">sp</font>,<font color="Olive" title="b3">cv</font>,<font color="Olive" title="b4">result</font>,<font color="Olive" title="b5">pp</font>,<font color="Olive" title="b6">pD</font>)</span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Olive" title="b1">s</font>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> (<span class="p2">(<span class="default"><font color="Olive" title="b1">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Olive" title="b2">sp</font></span>)</span></span>)</span>,<font color="Olive" title="b4">result</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <font color="Olive" title="b7">f</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">s</font> be   <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="memstr_0.html#V4" title="MEMSTR_0:attr.4">-started</a>  <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">sp</font>, <font color="Olive" title="b2">cv</font>, <font color="Olive" title="b3">result</font>, <font color="Olive" title="b4">pp</font>, <font color="Olive" title="b5">pD</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> <br/>  for <font color="Olive" title="b6">f</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Olive" title="b1">sp</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Olive" title="b1">sp</font> &amp; <font color="Olive" title="b2">cv</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b3">result</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Olive" title="b1">sp</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b3">result</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b4">pp</font> &amp; <font color="Olive" title="b4">pp</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b5">pD</font> &amp; <font color="Olive" title="b5">pD</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Olive" title="b5">pD</font></span>)</span> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b6">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Olive" title="b1">sp</font></span>)</span></span>)</span>,<font color="Olive" title="b2">cv</font>)</span>)</span> &amp; (  for <font color="Olive" title="b7">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="Olive" title="b7">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b6">f</font> holds <br/><font color="Olive" title="b6">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b7">k</font> <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="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Olive" title="b5">pD</font></span>)</span></span>)</span>,<font color="Olive" title="b7">k</font>)</span>)</span> ) holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><a href="scmpds_7.html#K4" title="SCMPDS_7:func.4">sum</a> (<font color="Olive" title="b1">sp</font>,<font color="Olive" title="b2">cv</font>,<font color="Olive" title="b3">result</font>,<font color="Olive" title="b4">pp</font>,<font color="Olive" title="b5">pD</font>)</span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Olive" title="b1">sp</font></span>)</span></span>)</span>,<font color="Olive" title="b3">result</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <font color="Olive" title="b6">f</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">sp</font>, <font color="Maroon" title="c6">cv</font>, <font color="Maroon" title="c7">fr</font>, <font color="Maroon" title="c8">pp</font>, <font color="Maroon" title="c9">pD</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">  for <font color="Olive" title="b1">f</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c5">sp</font> &amp; <font color="Maroon" title="c6">cv</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c7">fr</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c7">fr</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c8">pp</font> &amp; <font color="Maroon" title="c8">pp</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c9">pD</font> &amp; <font color="Maroon" title="c9">pD</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c9">pD</font></span>)</span> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span></span>)</span>,<font color="Maroon" title="c6">cv</font>)</span>)</span> &amp; (  for <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 <font color="Olive" title="b2">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">f</font> holds <br/><font color="Olive" title="b1">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">k</font> <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="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c9">pD</font></span>)</span></span>)</span>,<font color="Olive" title="b2">k</font>)</span>)</span> ) holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><a href="scmpds_7.html#K4" title="SCMPDS_7:func.4">sum</a> (<font color="Maroon" title="c5">sp</font>,<font color="Maroon" title="c6">cv</font>,<font color="Maroon" title="c7">fr</font>,<font color="Maroon" title="c8">pp</font>,<font color="Maroon" title="c9">pD</font>)</span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span></span>)</span>,<font color="Maroon" title="c7">fr</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <font color="Olive" title="b1">f</font></span><br/><span class="kw">let </span><font color="Maroon" title="c10">f</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</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="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c5">sp</font> &amp; <font color="Maroon" title="c6">cv</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c7">fr</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c7">fr</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c8">pp</font> &amp; <font color="Maroon" title="c8">pp</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c9">pD</font> &amp; <font color="Maroon" title="c9">pD</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c9">pD</font></span>)</span> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c10">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span></span>)</span>,<font color="Maroon" title="c6">cv</font>)</span>)</span> &amp; (  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="Olive" title="b1">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c10">f</font> holds <br/><font color="Maroon" title="c10">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">k</font> <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="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c9">pD</font></span>)</span></span>)</span>,<font color="Olive" title="b1">k</font>)</span>)</span> ) implies <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><a href="scmpds_7.html#K4" title="SCMPDS_7:func.4">sum</a> (<font color="Maroon" title="c5">sp</font>,<font color="Maroon" title="c6">cv</font>,<font color="Maroon" title="c7">fr</font>,<font color="Maroon" title="c8">pp</font>,<font color="Maroon" title="c9">pD</font>)</span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span></span>)</span>,<font color="Maroon" title="c7">fr</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <font color="Maroon" title="c10">f</font> )</span><br/>







<span class="kw">set </span><font color="Maroon" title="c11">BP</font> =  <a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c12">PD</font> =  <a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c9">pD</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c13">PP</font> =  <a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font>;<br/>
<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:67"/><span class="lab"><font color="Green" title="E48">A1</font></span>: 
<font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c5">sp</font>
 <span class="kw">and </span><br/><a NAME="E2:67"/><span class="lab"><font color="Green" title="E49">A2</font></span>: 
<font color="Maroon" title="c6">cv</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c7">fr</font>
 <span class="kw">and </span><br/><a NAME="E3:67"/><span class="lab"><font color="Green" title="E50">A3</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c7">fr</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c8">pp</font>
 <span class="kw">and </span><br/><a NAME="E4:67"/><span class="lab"><font color="Green" title="E51">A4</font></span>: 
<font color="Maroon" title="c8">pp</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c9">pD</font>
 <span class="kw">and </span><br/><a NAME="E5:67"/><span class="lab"><font color="Green" title="E52">A5</font></span>: 
<font color="Maroon" title="c9">pD</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c9">pD</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E6:67"/><span class="lab"><font color="Green" title="E53">A6</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c10">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span></span>)</span>,<font color="Maroon" title="c6">cv</font>)</span>)</span>
 <span class="kw">and </span><br/><a NAME="E7:67"/><span class="lab"><font color="Green" title="E54">A7</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="Olive" title="b1">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c10">f</font> holds <br/><font color="Maroon" title="c10">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">k</font> <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="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c9">pD</font></span>)</span></span>)</span>,<font color="Olive" title="b1">k</font>)</span>)</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="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><a href="scmpds_7.html#K4" title="SCMPDS_7:func.4">sum</a> (<font color="Maroon" title="c5">sp</font>,<font color="Maroon" title="c6">cv</font>,<font color="Maroon" title="c7">fr</font>,<font color="Maroon" title="c8">pp</font>,<font color="Maroon" title="c9">pD</font>)</span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span></span>)</span>,<font color="Maroon" title="c7">fr</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <font color="Maroon" title="c10">f</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c14">n</font> = <font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span> 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="txt" href="#E1:67"><span class="lab"><font color="Green" title="E48">A1</font></span></a>, <a class="ref" href="int_1.html#T3" title="INT_1:th.3">INT_1:3</a></span>;<br/>
<a NAME="E9:67"/><span class="lab"><font color="Green" title="E55">A8</font></span>: 
 <a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c9">pD</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:67"><span class="lab"><font color="Green" title="E51">A4</font></span></a>, <a class="ref" href="zfmisc_1.html#T27" title="ZFMISC_1:th.27">ZFMISC_1:27</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c15">i0</font> = (<span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>;<br/>
<span class="kw">set </span><font color="Maroon" title="c16">i1</font> = <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Maroon" title="c9">pD</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c17">Hi</font> = <span class="p1">(<span class="default">(<span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Maroon" title="c9">pD</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c18">i2</font> =  <a href="scmpds_2.html#K13" title="SCMPDS_2:func.13">AddTo</a> (<span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>,<span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c9">pD</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>);<br/>
<span class="kw">set </span><font color="Maroon" title="c19">i3</font> =  <a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> (<span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,1);<br/>
<span class="kw">set </span><font color="Maroon" title="c20">FD</font> =  <a href="scmpds_7.html#K2" title="SCMPDS_7:func.2">for-down</a> (<span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c6">cv</font>,1,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_2.html#K13" title="SCMPDS_2:func.13">AddTo</a> (<span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>,<span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c9">pD</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> (<span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,1)</span>)</span></span>)</span>);<br/>
<span class="kw">set </span><font color="Maroon" title="c21">s2</font> =  <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default">(<span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Maroon" title="c9">pD</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c22">P2</font> = <font color="Maroon" title="c3">P</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c23">s0</font> = <font color="Maroon" title="c4">s</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c24">s1</font> =  <a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p1">(<span class="default">(<span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>,<font color="Maroon" title="c4">s</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c25">a</font> =  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span></span>)</span>,<font color="Maroon" title="c7">fr</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c26">a1</font> =  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default">(<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Maroon" title="c9">pD</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span></span>)</span>,<font color="Maroon" title="c7">fr</font>);<br/>
<a NAME="E10:67"/><span class="lab"><font color="Green" title="E56">A9</font></span>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c7">fr</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmp_gcd.html#T1" title="SCMP_GCD:th.1">SCMP_GCD:1</a></span>;<br/>
<a NAME="E11:67"/><span class="kw">then </span><span class="lab"><font color="Green" title="E57">A10</font></span>: 
 <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c7">fr</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c7">fr</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T27" title="ZFMISC_1:th.27">ZFMISC_1:27</a></span>;<br/>
<a NAME="E12:67"/><span class="kw">then </span>
 <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c7">fr</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">sp</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:67"><span class="lab"><font color="Green" title="E48">A1</font></span></a>, <a class="ref" href="nat_1.html#T12" title="NAT_1:th.12">NAT_1:12</a></span>;<br/>
<a NAME="E13:67"/><span class="kw">then </span><span class="lab"><font color="Green" title="E58">A11</font></span>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T27" title="ZFMISC_1:th.27">ZFMISC_1:27</a></span>;<br/>
<a NAME="E14:67"/><span class="lab"><font color="Green" title="E59">A12</font></span>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c9">pD</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:67"><span class="lab"><font color="Green" title="E50">A3</font></span></a>, <a class="txt" href="#E4:67"><span class="lab"><font color="Green" title="E51">A4</font></span></a>, <a class="txt" href="#E10:67"><span class="lab"><font color="Green" title="E56">A9</font></span></a>, <a class="ref" href="zfmisc_1.html#T27" title="ZFMISC_1:th.27">ZFMISC_1:27</a></span>;<br/>
<span class="lab"><font color="Green" title="E60">A13</font></span>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default">(<span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Maroon" title="c9">pD</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c9">pD</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Maroon" title="c9">pD</font></span>)</span>,<span class="p2">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p3">(<span class="default">(<span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>,<font color="Maroon" title="c4">s</font>)</span>)</span>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c9">pD</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_5.html#T42" title="SCMPDS_5:th.42">SCMPDS_5:42</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p2">(<span class="default">(<span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c9">pD</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:67"><span class="lab"><font color="Green" title="E55">A8</font></span></a>, <a class="ref" href="scmpds_2.html#T45" title="SCMPDS_2:th.45">SCMPDS_2:45</a></span>
<br/>.= 
<font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c9">pD</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:67"><span class="lab"><font color="Green" title="E59">A12</font></span></a>, <a class="ref" href="scmpds_2.html#T46" title="SCMPDS_2:th.46">SCMPDS_2:46</a></span>
;<br/>
<a NAME="E16:67"/>
<font color="Maroon" title="c14">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c14">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c7">fr</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T12" title="NAT_1:th.12">NAT_1:12</a></span>;<br/>
<a NAME="E17:67"/><span class="kw">then </span>
<font color="Maroon" title="c5">sp</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">pp</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:67"><span class="lab"><font color="Green" title="E48">A1</font></span></a>, <a class="txt" href="#E3:67"><span class="lab"><font color="Green" title="E50">A3</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/>
<a NAME="E18:67"/><span class="kw">then </span><span class="lab"><font color="Green" title="E61">A14</font></span>: 
 <a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T27" title="ZFMISC_1:th.27">ZFMISC_1:27</a></span>;<br/>
<a NAME="E19:67"/><span class="lab"><font color="Green" title="E62">A15</font></span>: 
 <a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c7">fr</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:67"><span class="lab"><font color="Green" title="E50">A3</font></span></a>, <a class="ref" href="zfmisc_1.html#T27" title="ZFMISC_1:th.27">ZFMISC_1:27</a></span>;<br/>
<span class="lab"><font color="Green" title="E63">A16</font></span>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default">(<span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Maroon" title="c9">pD</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Maroon" title="c9">pD</font></span>)</span>,<span class="p2">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p3">(<span class="default">(<span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>,<font color="Maroon" title="c4">s</font>)</span>)</span>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_5.html#T42" title="SCMPDS_5:th.42">SCMPDS_5:42</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p2">(<span class="default">(<span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:67"><span class="lab"><font color="Green" title="E61">A14</font></span></a>, <a class="ref" href="scmpds_2.html#T45" title="SCMPDS_2:th.45">SCMPDS_2:45</a></span>
<br/>.= 
<font color="Maroon" title="c14">n</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:67"><span class="lab"><font color="Green" title="E58">A11</font></span></a>, <a class="ref" href="scmpds_2.html#T46" title="SCMPDS_2:th.46">SCMPDS_2:46</a></span>
;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E64">A17</font></span>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default">(<span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Maroon" title="c9">pD</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p4">(<span class="default"><span class="p5">(<span class="default">(<span class="p0">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Maroon" title="c9">pD</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span></span>)</span>,<font color="Maroon" title="c7">fr</font>)</span>)</span> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default">(<span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Maroon" title="c9">pD</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon" title="c14">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c7">fr</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmp_gcd.html#T1" title="SCMP_GCD:th.1">SCMP_GCD:1</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Maroon" title="c9">pD</font></span>)</span>,<span class="p2">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p3">(<span class="default">(<span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>,<font color="Maroon" title="c4">s</font>)</span>)</span>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon" title="c14">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c7">fr</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_5.html#T42" title="SCMPDS_5:th.42">SCMPDS_5:42</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p2">(<span class="default">(<span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon" title="c14">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c7">fr</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:67"><span class="lab"><font color="Green" title="E62">A15</font></span></a>, <a class="ref" href="scmpds_2.html#T45" title="SCMPDS_2:th.45">SCMPDS_2:45</a></span>
<br/>.= 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:67"><span class="lab"><font color="Green" title="E56">A9</font></span></a>, <a class="ref" href="scmpds_2.html#T46" title="SCMPDS_2:th.46">SCMPDS_2:46</a></span>
;<br/>
<a NAME="E22:67"/><span class="lab"><font color="Green" title="E65">A18</font></span>: 
<font color="Maroon" title="c14">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c7">fr</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c9">pD</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:67"><span class="lab"><font color="Green" title="E50">A3</font></span></a>, <a class="txt" href="#E4:67"><span class="lab"><font color="Green" title="E51">A4</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E66">A19</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="67_4"><span class="kw">now </span></a><div class="add"><span class="kw">reconsider </span><font color="Maroon" title="c27">m</font> = <font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c9">pD</font></span>)</span> 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="txt" href="#E5:67"><span class="lab"><font color="Green" title="E52">A5</font></span></a>, <a class="ref" href="int_1.html#T3" title="INT_1:th.3">INT_1:3</a></span>;<br/><span class="kw">let </span><font color="Maroon" title="c28">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" title="c28">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c10">f</font> implies <span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default">(<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Maroon" title="c9">pD</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p4">(<span class="default"><span class="p5">(<span class="default">(<span class="p0">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Maroon" title="c9">pD</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c9">pD</font></span>)</span></span>)</span>,<font color="Maroon" title="c28">k</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c28">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> )</span><br/><span class="kw">assume </span><a NAME="E2:67_4"/><span class="lab"><font color="Green" title="E67">A20</font></span>: 
<font color="Maroon" title="c28">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c10">f</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="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default">(<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Maroon" title="c9">pD</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p4">(<span class="default"><span class="p5">(<span class="default">(<span class="p0">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Maroon" title="c9">pD</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c9">pD</font></span>)</span></span>)</span>,<font color="Maroon" title="c28">k</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c28">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span><br/><a NAME="E3:67_4"/>
<font color="Maroon" title="c8">pp</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c27">m</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:67"><span class="lab"><font color="Green" title="E51">A4</font></span></a>, <a class="txt" href="#E5:67"><span class="lab"><font color="Green" title="E52">A5</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/><a NAME="E4:67_4"/><span class="kw">then </span>
<font color="Maroon" title="c27">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c28">k</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">pp</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></span>;<br/><a NAME="E5:67_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E68">A21</font></span>: 
 <a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p1">(<span class="default"><font color="Maroon" title="c27">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c28">k</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T27" title="ZFMISC_1:th.27">ZFMISC_1:27</a></span>;<br/><a NAME="E6:67_4"/>
<font color="Maroon" title="c27">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c27">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c28">k</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></span>;<br/><a NAME="E7:67_4"/><span class="kw">then </span>
 <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c7">fr</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c27">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c28">k</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:67"><span class="lab"><font color="Green" title="E52">A5</font></span></a>, <a class="txt" href="#E11:67"><span class="lab"><font color="Green" title="E57">A10</font></span></a>, <a class="txt" href="#E22:67"><span class="lab"><font color="Green" title="E65">A18</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/><a NAME="E8:67_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E69">A22</font></span>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p1">(<span class="default"><font color="Maroon" title="c27">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c28">k</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T27" title="ZFMISC_1:th.27">ZFMISC_1:27</a></span>;<br/><span class="kw">thus </span><span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default">(<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Maroon" title="c9">pD</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p4">(<span class="default"><span class="p5">(<span class="default">(<span class="p0">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Maroon" title="c9">pD</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c9">pD</font></span>)</span></span>)</span>,<font color="Maroon" title="c28">k</font>)</span>)</span> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default">(<span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Maroon" title="c9">pD</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p4">(<span class="default"><span class="p5">(<span class="default">(<span class="p0">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Maroon" title="c9">pD</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c9">pD</font></span>)</span></span>)</span>,<font color="Maroon" title="c28">k</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_5.html#T15" title="SCMPDS_5:th.15">SCMPDS_5:15</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default">(<span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Maroon" title="c9">pD</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon" title="c27">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c28">k</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:67"><span class="lab"><font color="Green" title="E60">A13</font></span></a>, <a class="ref" href="scmp_gcd.html#T1" title="SCMP_GCD:th.1">SCMP_GCD:1</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Maroon" title="c9">pD</font></span>)</span>,<span class="p2">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p3">(<span class="default">(<span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>,<font color="Maroon" title="c4">s</font>)</span>)</span>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon" title="c27">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c28">k</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_5.html#T42" title="SCMPDS_5:th.42">SCMPDS_5:42</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p2">(<span class="default">(<span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon" title="c27">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c28">k</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:67_4"><span class="lab"><font color="Green" title="E68">A21</font></span></a>, <a class="ref" href="scmpds_2.html#T45" title="SCMPDS_2:th.45">SCMPDS_2:45</a></span>
<br/>.= 
<font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon" title="c27">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c28">k</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:67_4"><span class="lab"><font color="Green" title="E69">A22</font></span></a>, <a class="ref" href="scmpds_2.html#T46" title="SCMPDS_2:th.46">SCMPDS_2:46</a></span>
<br/>.= 
<font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c9">pD</font></span>)</span></span>)</span>,<font color="Maroon" title="c28">k</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmp_gcd.html#T1" title="SCMP_GCD:th.1">SCMP_GCD:1</a></span>
<br/>.= 
<font color="Maroon" title="c10">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c28">k</font> <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="#E7:67"><span class="lab"><font color="Green" title="E54">A7</font></span></a>, <a class="txt" href="#E2:67_4"><span class="lab"><font color="Green" title="E67">A20</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>
<a NAME="E24:67"/>
 <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c7">fr</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c6">cv</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:67"><span class="lab"><font color="Green" title="E49">A2</font></span></a>, <a class="txt" href="#E11:67"><span class="lab"><font color="Green" title="E57">A10</font></span></a></span>;<br/>
<a NAME="E25:67"/><span class="kw">then </span><span class="lab"><font color="Green" title="E67">A23</font></span>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c6">cv</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T27" title="ZFMISC_1:th.27">ZFMISC_1:27</a></span>;<br/>
<a NAME="E26:67"/>
<font color="Maroon" title="c14">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c6">cv</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">pp</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:67"><span class="lab"><font color="Green" title="E49">A2</font></span></a>, <a class="txt" href="#E3:67"><span class="lab"><font color="Green" title="E50">A3</font></span></a>, <a class="ref" href="xreal_1.html#T6" title="XREAL_1:th.6">XREAL_1:6</a></span>;<br/>
<a NAME="E27:67"/><span class="kw">then </span><span class="lab"><font color="Green" title="E68">A24</font></span>: 
 <a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c6">cv</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T27" title="ZFMISC_1:th.27">ZFMISC_1:27</a></span>;<br/>
<a NAME="E28:67"/><span class="lab"><font color="Green" title="E69">A25</font></span>: 
<span class="p1">(<span class="default">(<span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Maroon" title="c9">pD</font></span>)</span> <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_6.html#T21" title="SCMPDS_6:th.21">SCMPDS_6:21</a></span>;<br/>
<a NAME="E29:67"/><span class="lab"><font color="Green" title="E70">A26</font></span>: 
<span class="p1">(<span class="default">(<span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Maroon" title="c9">pD</font></span>)</span> <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_6.html#T20" title="SCMPDS_6:th.20">SCMPDS_6:20</a></span>;<br/>
<a NAME="E30:67"/><span class="lab"><font color="Green" title="E71">A27</font></span>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default">(<span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Maroon" title="c9">pD</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default">(<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Maroon" title="c9">pD</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_5.html#T15" title="SCMPDS_5:th.15">SCMPDS_5:15</a></span>;<br/>
<a NAME="E31:67"/><span class="lab"><font color="Green" title="E72">A28</font></span>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default">(<span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Maroon" title="c9">pD</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default">(<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Maroon" title="c9">pD</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_5.html#T15" title="SCMPDS_5:th.15">SCMPDS_5:15</a></span>;<br/>
<a NAME="E32:67"/><span class="lab"><font color="Green" title="E73">A29</font></span>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default">(<span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Maroon" title="c9">pD</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c9">pD</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default">(<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Maroon" title="c9">pD</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c9">pD</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_5.html#T15" title="SCMPDS_5:th.15">SCMPDS_5:15</a></span>;<br/>
<span class="lab"><font color="Green" title="E74">A30</font></span>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default">(<span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Maroon" title="c9">pD</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Maroon" title="c9">pD</font></span>)</span>,<span class="p2">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p3">(<span class="default">(<span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>,<font color="Maroon" title="c4">s</font>)</span>)</span>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_5.html#T42" title="SCMPDS_5:th.42">SCMPDS_5:42</a></span>
<br/>.= 
<font color="Maroon" title="c9">pD</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_2.html#T45" title="SCMPDS_2:th.45">SCMPDS_2:45</a></span>
;<br/>
<a NAME="E34:67"/><span class="kw">then </span>
 <a href="scmpds_7.html#K2" title="SCMPDS_7:func.2">for-down</a> (<span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c6">cv</font>,1,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_2.html#K13" title="SCMPDS_2:func.13">AddTo</a> (<span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>,<span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c9">pD</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> (<span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,1)</span>)</span></span>)</span>) <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a>  <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default">(<span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Maroon" title="c9">pD</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span>,<font color="Maroon" title="c3">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:67"><span class="lab"><font color="Green" title="E48">A1</font></span></a>, <a class="txt" href="#E2:67"><span class="lab"><font color="Green" title="E49">A2</font></span></a>, <a class="txt" href="#E3:67"><span class="lab"><font color="Green" title="E50">A3</font></span></a>, <a class="txt" href="#E4:67"><span class="lab"><font color="Green" title="E51">A4</font></span></a>, <a class="txt" href="#E5:67"><span class="lab"><font color="Green" title="E52">A5</font></span></a>, <a class="txt" href="#E20:67"><span class="lab"><font color="Green" title="E63">A16</font></span></a>, <a class="txt" href="#E15:67"><span class="lab"><font color="Green" title="E60">A13</font></span></a>, <a class="ref" href="scmpds_7.html#T53" target="_self" title="SCMPDS_7:th.53">Th72</a>, <a class="txt" href="#E30:67"><span class="lab"><font color="Green" title="E71">A27</font></span></a>, <a class="txt" href="#E31:67"><span class="lab"><font color="Green" title="E72">A28</font></span></a>, <a class="txt" href="#E32:67"><span class="lab"><font color="Green" title="E73">A29</font></span></a></span>;<br/>
<a NAME="E35:67"/><span class="kw">then </span><span class="lab"><font color="Green" title="E75">A31</font></span>: 
 <a href="scmpds_7.html#K2" title="SCMPDS_7:func.2">for-down</a> (<span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c6">cv</font>,1,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_2.html#K13" title="SCMPDS_2:func.13">AddTo</a> (<span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>,<span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c9">pD</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> (<span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,1)</span>)</span></span>)</span>) <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a>  <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default">(<span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Maroon" title="c9">pD</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>),<font color="Maroon" title="c3">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_6.html#T126" title="SCMPDS_6:th.126">SCMPDS_6:126</a></span>;<br/>
<span class="lab"><font color="Green" title="E76">A32</font></span>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default">(<span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Maroon" title="c9">pD</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p4">(<span class="default"><span class="p5">(<span class="default">(<span class="p0">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Maroon" title="c9">pD</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span></span>)</span>,<font color="Maroon" title="c6">cv</font>)</span>)</span> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default">(<span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Maroon" title="c9">pD</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon" title="c14">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c6">cv</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:67"><span class="lab"><font color="Green" title="E63">A16</font></span></a>, <a class="ref" href="scmp_gcd.html#T1" title="SCMP_GCD:th.1">SCMP_GCD:1</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Maroon" title="c9">pD</font></span>)</span>,<span class="p2">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p3">(<span class="default">(<span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>,<font color="Maroon" title="c4">s</font>)</span>)</span>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon" title="c14">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c6">cv</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_5.html#T42" title="SCMPDS_5:th.42">SCMPDS_5:42</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p2">(<span class="default">(<span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon" title="c14">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c6">cv</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:67"><span class="lab"><font color="Green" title="E68">A24</font></span></a>, <a class="ref" href="scmpds_2.html#T45" title="SCMPDS_2:th.45">SCMPDS_2:45</a></span>
<br/>.= 
<font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon" title="c14">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c6">cv</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E25:67"><span class="lab"><font color="Green" title="E67">A23</font></span></a>, <a class="ref" href="scmpds_2.html#T46" title="SCMPDS_2:th.46">SCMPDS_2:46</a></span>
<br/>.= 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c10">f</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:67"><span class="lab"><font color="Green" title="E53">A6</font></span></a>, <a class="ref" href="scmp_gcd.html#T1" title="SCMP_GCD:th.1">SCMP_GCD:1</a></span>
;<br/>
<a NAME="E37:67"/><span class="lab"><font color="Green" title="E77">A33</font></span>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default">(<span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Maroon" title="c9">pD</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p4">(<span class="default"><span class="p5">(<span class="default">(<span class="p0">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Maroon" title="c9">pD</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span></span>)</span>,<font color="Maroon" title="c7">fr</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default">(<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Maroon" title="c9">pD</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p4">(<span class="default"><span class="p5">(<span class="default">(<span class="p0">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Maroon" title="c9">pD</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span></span>)</span>,<font color="Maroon" title="c7">fr</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_5.html#T15" title="SCMPDS_5:th.15">SCMPDS_5:15</a></span>;<br/>
<a NAME="E38:67"/><span class="lab"><font color="Green" title="E78">A34</font></span>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default">(<span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Maroon" title="c9">pD</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p4">(<span class="default"><span class="p5">(<span class="default">(<span class="p0">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Maroon" title="c9">pD</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span></span>)</span>,<font color="Maroon" title="c6">cv</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default">(<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Maroon" title="c9">pD</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p4">(<span class="default"><span class="p5">(<span class="default">(<span class="p0">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Maroon" title="c9">pD</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span></span>)</span>,<font color="Maroon" title="c6">cv</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_5.html#T15" title="SCMPDS_5:th.15">SCMPDS_5:15</a></span>;<br/>
<a NAME="E39:67"/>
 <a href="scmpds_7.html#K2" title="SCMPDS_7:func.2">for-down</a> (<span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c6">cv</font>,1,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_2.html#K13" title="SCMPDS_2:func.13">AddTo</a> (<span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>,<span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c9">pD</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> (<span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,1)</span>)</span></span>)</span>) <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a>  <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default">(<span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Maroon" title="c9">pD</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span>,<font color="Maroon" title="c3">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:67"><span class="lab"><font color="Green" title="E48">A1</font></span></a>, <a class="txt" href="#E2:67"><span class="lab"><font color="Green" title="E49">A2</font></span></a>, <a class="txt" href="#E3:67"><span class="lab"><font color="Green" title="E50">A3</font></span></a>, <a class="txt" href="#E4:67"><span class="lab"><font color="Green" title="E51">A4</font></span></a>, <a class="txt" href="#E5:67"><span class="lab"><font color="Green" title="E52">A5</font></span></a>, <a class="txt" href="#E20:67"><span class="lab"><font color="Green" title="E63">A16</font></span></a>, <a class="txt" href="#E33:67"><span class="lab"><font color="Green" title="E74">A30</font></span></a>, <a class="txt" href="#E15:67"><span class="lab"><font color="Green" title="E60">A13</font></span></a>, <a class="ref" href="scmpds_7.html#T53" target="_self" title="SCMPDS_7:th.53">Th72</a>, <a class="txt" href="#E30:67"><span class="lab"><font color="Green" title="E71">A27</font></span></a>, <a class="txt" href="#E31:67"><span class="lab"><font color="Green" title="E72">A28</font></span></a>, <a class="txt" href="#E32:67"><span class="lab"><font color="Green" title="E73">A29</font></span></a></span>;<br/>
<a NAME="E40:67"/><span class="kw">then </span>
 <a href="scmpds_7.html#K2" title="SCMPDS_7:func.2">for-down</a> (<span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c6">cv</font>,1,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_2.html#K13" title="SCMPDS_2:func.13">AddTo</a> (<span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>,<span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c9">pD</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> (<span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,1)</span>)</span></span>)</span>) <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a>  <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default">(<span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Maroon" title="c9">pD</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>),<font color="Maroon" title="c3">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_6.html#T125" title="SCMPDS_6:th.125">SCMPDS_6:125</a></span>;<br/>
<span class="kw">hence </span><span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><a href="scmpds_7.html#K4" title="SCMPDS_7:func.4">sum</a> (<font color="Maroon" title="c5">sp</font>,<font color="Maroon" title="c6">cv</font>,<font color="Maroon" title="c7">fr</font>,<font color="Maroon" title="c8">pp</font>,<font color="Maroon" title="c9">pD</font>)</span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span></span>)</span>,<font color="Maroon" title="c7">fr</font>)</span>)</span> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p2">(<span class="default"><a href="scmpds_7.html#K2" title="SCMPDS_7:func.2">for-down</a> (<span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c6">cv</font>,1,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmpds_2.html#K13" title="SCMPDS_2:func.13">AddTo</a> (<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c9">pD</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> (<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,1)</span>)</span></span>)</span>)</span>)</span>,<font color="Maroon" title="c3">P</font>,<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="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p4">(<span class="default"><span class="p5">(<span class="default">(<span class="p0">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Maroon" title="c9">pD</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span></span>)</span>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<span class="p4">(<span class="default"><span class="p5">(<span class="default">(<span class="p0">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span>,<font color="Maroon" title="c7">fr</font>) <a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmpds_4.html#K4" title="SCMPDS_4:func.4">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c8">pp</font></span>)</span> <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <font color="Maroon" title="c9">pD</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c5">sp</font></span>)</span></span>)</span>,<font color="Maroon" title="c7">fr</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:67"><span class="lab"><font color="Green" title="E63">A16</font></span></a>, <a class="txt" href="#E29:67"><span class="lab"><font color="Green" title="E70">A26</font></span></a>, <a class="txt" href="#E28:67"><span class="lab"><font color="Green" title="E69">A25</font></span></a>, <a class="txt" href="#E35:67"><span class="lab"><font color="Green" title="E75">A31</font></span></a>, <a class="ref" href="scmpds_7.html#T30" target="_self" title="SCMPDS_7:th.30">Th49</a></span>
<br/>.= 
 <a href="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <font color="Maroon" title="c10">f</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:67"><span class="lab"><font color="Green" title="E48">A1</font></span></a>, <a class="txt" href="#E2:67"><span class="lab"><font color="Green" title="E49">A2</font></span></a>, <a class="txt" href="#E3:67"><span class="lab"><font color="Green" title="E50">A3</font></span></a>, <a class="txt" href="#E4:67"><span class="lab"><font color="Green" title="E51">A4</font></span></a>, <a class="txt" href="#E5:67"><span class="lab"><font color="Green" title="E52">A5</font></span></a>, <a class="txt" href="#E20:67"><span class="lab"><font color="Green" title="E63">A16</font></span></a>, <a class="txt" href="#E33:67"><span class="lab"><font color="Green" title="E74">A30</font></span></a>, <a class="txt" href="#E15:67"><span class="lab"><font color="Green" title="E60">A13</font></span></a>, <a class="txt" href="#E21:67"><span class="lab"><font color="Green" title="E64">A17</font></span></a>, <a class="txt" href="#E36:67"><span class="lab"><font color="Green" title="E76">A32</font></span></a>, <a class="txt" href="#E23:67"><span class="lab"><font color="Green" title="E66">A19</font></span></a>, <a class="ref" href="scmpds_7.html#T54" target="_self" title="SCMPDS_7:th.54">Th73</a>, <a class="txt" href="#E30:67"><span class="lab"><font color="Green" title="E71">A27</font></span></a>, <a class="txt" href="#E31:67"><span class="lab"><font color="Green" title="E72">A28</font></span></a>, <a class="txt" href="#E32:67"><span class="lab"><font color="Green" title="E73">A29</font></span></a>, <a class="txt" href="#E37:67"><span class="lab"><font color="Green" title="E77">A33</font></span></a>, <a class="txt" href="#E38:67"><span class="lab"><font color="Green" title="E78">A34</font></span></a></span>
;<br/> <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>
