Thm*
L:LangOver(Alph).
Fin(Alph) ![]()
Fin(x,y:Alph*//L-induced Equiv(x,y)) & (
l:Alph*. Dec(L(l))) ![]()
(
St:Type, Auto:Automata(Alph;St). Fin(St) & L = LangOf(Auto))
mn_31
Thm*
L:LangOver(Alph).
Fin(Alph) ![]()
(
St:Type, Auto:Automata(Alph;St). Fin(St) & L = LangOf(Auto)) ![]()
(
R:(Alph*![]()
Alph*![]()
Prop).
(EquivRel x,y:Alph*. x R y) c
(
g:((x,y:Alph*//R(x,y))![]()
![]()
).
Fin(x,y:Alph*//R(x,y))
& (
l:Alph*. L(l) ![]()
g(l))
& (
x,y,z:Alph*. R(x,y) ![]()
R((z @ x),z @ y))))
mn_12