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1.
Alph:
Type
2.
L:
LangOver(Alph)
3.
EquivRel x,y:Alph*. x L-induced Equiv y
4.
Fin(Alph)
5.
Fin(x,y:Alph*//L-induced Equiv(x,y))
6.
l:Alph*. Dec(L(l))
Auto:Automata(Alph;x,y:Alph*//L-induced Equiv(x,y)). Fin(x,y:Alph*//L-induced Equiv(x,y)) & L = LangOf(Auto)
By:
Inst
Thm*
f:(T
Prop). (
t:T. Dec(f(t)))
(
g:(T
).
t:T. f(t)
g(t)) [Alph*;L] THENA (Auto THEN Fold `languages` 0)
Generated subgoal:
1
7.
g:(Alph*
).
t:Alph*. L(t)
g(t)
Auto:Automata(Alph;x,y:Alph*//L-induced Equiv(x,y)). Fin(x,y:Alph*//L-induced Equiv(x,y)) & L = LangOf(Auto)
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