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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E44">Th48</font></span>: <a NAME="T50"><span class="comment"><font color="firebrick">:: SCMPDS_7:50</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>  st <font color="Olive" title="b2">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  holds <br/>(  <a href="scmpds_7.html#K2" title="SCMPDS_7:func.2">for-down</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2,1,<span class="p1">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">Load</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">AddTo</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,1)</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> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,2,1,<span class="p1">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">Load</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K11" title="SCMPDS_2:func.11">AddTo</a> (<a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>,3,1)</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>
