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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E12">Th18</font></span>: <a NAME="T18"><span class="comment"><font color="firebrick">:: FSM_2:18</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">I</font>, <font color="Olive" title="b2">O</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b3">s</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">I</font><br/>  for <font color="Olive" title="b4">M</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="fsm_2.html#L2" title="FSM_2:struct.2">Moore-SM_Final</a> over <font color="Olive" title="b1">I</font>,<font color="Olive" title="b2">O</font>  st <font color="Olive" title="b4">M</font> is  <a href="fsm_2.html#V1" title="FSM_2:attr.1">calculating_type</a>  &amp; <font color="Olive" title="b3">s</font> <a href="fsm_2.html#R2" title="FSM_2:pred.2">leads_to_final_state_of</a> <font color="Olive" title="b4">M</font> holds <br/> ex <font color="Olive" title="b5">m</font> being   non  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</a>   <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 <br/>( (  for <font color="Olive" title="b6">w</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Olive" title="b1">I</font>  st <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b6">w</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Olive" title="b5">m</font> &amp; <font color="Olive" title="b6">w</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">s</font> holds <br/><span class="p1">(<span class="default"><a href="fsm_2.html#NK1" title="FSM_2:NK.1">GEN</a> (<font color="Olive" title="b6">w</font>, the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <font color="Olive" title="b4">M</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">m</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="fsm_2.html#U1" title="FSM_2:sel.1">FinalS</a> of <font color="Olive" title="b4">M</font> ) &amp; (  for <font color="Olive" title="b6">w</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Olive" title="b1">I</font><br/>  for <font color="Olive" title="b7">j</font> being   non  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</a>   <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="b7">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b6">w</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 &amp; <font color="Olive" title="b6">w</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">s</font> &amp; <font color="Olive" title="b7">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b5">m</font> holds <br/> not <span class="p1">(<span class="default"><a href="fsm_2.html#NK1" title="FSM_2:NK.1">GEN</a> (<font color="Olive" title="b6">w</font>, the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <font color="Olive" title="b4">M</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b7">j</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="fsm_2.html#U1" title="FSM_2:sel.1">FinalS</a> of <font color="Olive" title="b4">M</font> ) )</div></div>
