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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E19">Th19</font></span>: <a NAME="T19"><span class="comment"><font color="firebrick">:: TURING_1:19</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">T</font> being    <a href="turing_1.html#L1" title="TURING_1:struct.1">TuringStr</a> <br/>  for <font color="Olive" title="b2">t</font> being   <a href="turing_1.html#NM2" title="TURING_1:NM.2">Tape</a> of <font color="Olive" title="b1">T</font><br/>  for <font color="Olive" title="b3">s</font>, <font color="Olive" title="b4">n1</font>, <font color="Olive" title="b5">n2</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>   st <font color="Olive" title="b2">t</font> <a href="turing_1.html#R2" title="TURING_1:pred.2">storeData</a> <span class="p1"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Olive" title="b3">s</font>,<font color="Olive" title="b4">n1</font>,<font color="Olive" title="b5">n2</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span> holds <br/>( <font color="Olive" title="b2">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Olive" title="b2">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b3">s</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Olive" title="b4">n1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Olive" title="b2">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b3">s</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Olive" title="b4">n1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Olive" title="b5">n2</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; (  for <font color="Olive" title="b6">i</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>  st <font color="Olive" title="b3">s</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b6">i</font> &amp; <font color="Olive" title="b6">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">s</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Olive" title="b4">n1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2 holds <br/><font color="Olive" title="b2">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) &amp; (  for <font color="Olive" title="b6">i</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>  st <span class="p1">(<span class="default"><font color="Olive" title="b3">s</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Olive" title="b4">n1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b6">i</font> &amp; <font color="Olive" title="b6">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b3">s</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Olive" title="b4">n1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Olive" title="b5">n2</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4 holds <br/><font color="Olive" title="b2">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) )</div></div>
