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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E46">Th51</font></span>: <a NAME="T53"><span class="comment"><font color="firebrick">:: SCMPDS_7:53</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">P</font> being   <a href="compos_1.html#NM2" title="COMPOS_1:NM.2">Instruction-Sequence</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a><br/>  for <font color="Olive" title="b2">s</font> being   <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="memstr_0.html#V5" title="MEMSTR_0:attr.5">-started</a>  <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a><br/>  for <font color="Olive" title="b3">sp</font>, <font color="Olive" title="b4">cv</font>, <font color="Olive" title="b5">result</font>, <font color="Olive" title="b6">pp</font>, <font color="Olive" title="b7">pD</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b2">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Olive" title="b3">sp</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Olive" title="b3">sp</font> &amp; <font color="Olive" title="b4">cv</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b5">result</font> &amp; <font color="Olive" title="b2">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</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">pp</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b7">pD</font> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b2">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Olive" title="b3">sp</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b5">result</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b6">pp</font> &amp; <font color="Olive" title="b6">pp</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b7">pD</font> &amp; <font color="Olive" title="b7">pD</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b2">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Olive" title="b7">pD</font></span>)</span> holds <br/>(  <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="Olive" title="b3">sp</font></span>)</span>,<font color="Olive" title="b4">cv</font>,1,<span class="p1">(<span class="default"><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="Olive" title="b3">sp</font></span>)</span>,<font color="Olive" title="b5">result</font>,<span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Olive" title="b7">pD</font></span>)</span>,<a href="numbers.html#K5" title="NUMBERS:func.5">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#K11" title="SCMPDS_2:func.11">AddTo</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">pp</font></span>)</span>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1)</span>)</span></span>)</span>) <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Olive" title="b2">s</font>,<font color="Olive" title="b1">P</font> &amp;  <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="Olive" title="b3">sp</font></span>)</span>,<font color="Olive" title="b4">cv</font>,1,<span class="p1">(<span class="default"><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="Olive" title="b3">sp</font></span>)</span>,<font color="Olive" title="b5">result</font>,<span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Olive" title="b7">pD</font></span>)</span>,<a href="numbers.html#K5" title="NUMBERS:func.5">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#K11" title="SCMPDS_2:func.11">AddTo</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">pp</font></span>)</span>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1)</span>)</span></span>)</span>) <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Olive" title="b2">s</font>,<font color="Olive" title="b1">P</font> )</div></div>
