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Definitions
myhill
nerode
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AutomataTheory
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1
2
1
1
1.
Alph:
Type
2.
S:
ActionSet(Alph)
3.
s:
S.car
4.
n:
5.
f:
n
Alph
6.
Bij(
n; Alph; f)
7.
n1:
8.
f1:
n1
S.car
9.
Bij(
n1; S.car; f1)
10.
BL:S.car*.
t:S.car. mem_f(S.car;t;BL)
(
i:
||(
x. < f1(x),(
y.S.act(f(y),f1(x)))[
n] > )[
n1]||. 1of(((
x. < f1(x),(
y.S.act(f(y),f1(x)))[
n] > )[
n1])[i]) = t & mem_f(S.car;s;2of(((
x. < f1(x),(
y.S.act(f(y),f1(x)))[
n] > )[
n1])[i])))
BL:S.car*.
t:S.car. mem_f(S.car;t;BL)
(
a:Alph. S.act(a,t) = s)
By:
RWH (LemmaC
Thm*
n:
, f:(
n
T), i:
n. ((f)[
n])[i] = f(i)) -1
THEN
Reduce -1
THEN
Analyze -1
Generated subgoal:
1
10.
BL:
S.car*
11.
t:S.car. mem_f(S.car;t;BL)
(
i:
||(
x. < f1(x),(
y.S.act(f(y),f1(x)))[
n] > )[
n1]||. f1(i) = t & mem_f(S.car;s;(
y.S.act(f(y),f1(i)))[
n]))
BL:S.car*.
t:S.car. mem_f(S.car;t;BL)
(
a:Alph. S.act(a,t) = s)
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