Thm*
E:(Alph*![]()
Alph*![]()
Prop).
Fin(Alph) & (EquivRel x,y:Alph*. x E y) & (
x,y:Alph*. Dec(x E y)) ![]()
(
h:(Alph*![]()
Alph*).
(
x,y:Alph*. (x E y) ![]()
h(x) = h(y)) & (
x:Alph*. x E (h(x))))
fin_alph_list_quo
Thm*
q:
, E:(
q*![]()
![]()
q*![]()
Prop).
(EquivRel x,y:
q*. x E y) & (
x,y:
q*. Dec(x E y)) ![]()
(
h:(
q*![]()
![]()
q*).
(
x,y:
q*. (x E y) ![]()
h(x) = h(y)) & (
x:
q*. x E (h(x))))
list_quo_choice
Thm*
q:![]()
, E:(
q*![]()
![]()
q*![]()
Prop).
(EquivRel x,y:
q*. x E y) & (
x,y:
q*. Dec(x E y)) ![]()
(
h:(
q*![]()
![]()
q*).
(
x,y:
q*. (x E y) ![]()
h(x) = h(y)) & (
x:
q*. x E (h(x))))
list_quo_choice_pls
Thm*
Auto:Automata(Alph;St).
Fin(Alph) & Fin(St) ![]()
(
x,y:Alph*.
Dec(x = y
x,y:Alph*//(x LangOf(Auto)-induced Equiv y)))
Rl_quo_is_decidable
In prior sections: core int 1 bool 1 rel 1 choice 1 int 2 finite sets list 3 autom exponent quot 1 relation autom det automata myhill nerode