<?xml version="1.0"?>
<div>:: <span class="kw">deftheorem </span>   defines <a href="fsm_2.html#V1" title="FSM_2:attr.1">calculating_type</a> <a onclick="hs(this)" href="javascript:()">FSM_2:def 1 : <br/></a><span> for <font color="Olive" title="b1">I</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="b2">S</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="fsm_1.html#L1" title="FSM_1:struct.1">FSM</a> over <font color="Olive" title="b1">I</font> holds <br/> ( <font color="Olive" title="b2">S</font> is  <a href="fsm_2.html#V1" title="FSM_2:attr.1">calculating_type</a>  iff  for <font color="Olive" title="b3">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> <br/>  for <font color="Olive" title="b4">w1</font>, <font color="Olive" title="b5">w2</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Olive" title="b1">I</font>  st <font color="Olive" title="b4">w1</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="b5">w2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 &amp; <font color="Olive" title="b3">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="b4">w1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 &amp; <font color="Olive" title="b3">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="b5">w2</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 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="b4">w1</font>, the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <font color="Olive" title="b2">S</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="fsm_2.html#NK1" title="FSM_2:NK.1">GEN</a> (<font color="Olive" title="b5">w2</font>, the <a href="fsm_1.html#U2" title="FSM_1:sel.2">InitS</a> of <font color="Olive" title="b2">S</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">j</font> );<br/></span></div>
