PrintForm Definitions myhill nerode Sections AutomataTheory Doc

At: mn 23 lem 1 1 1 1 2 1 1 2 2 2 2 1 1 2 1 2 2
1. Alph: Type
2. R: Alph*Alph*Prop
3. Fin(Alph)
4. EquivRel x,y:Alph*. x R y
5. Fin(x,y:Alph*//(x R y))
6. x,y,z:Alph*. (x R y) ((z @ x) R (z @ y))
7. g: (x,y:Alph*//(x R y))
8. x: x,y:Alph*//(x R y)
9. y: x,y:Alph*//(x R y)
10. Fin((x,y:Alph*//(x R y))(x,y:Alph*//(x R y)))
11. RL: ((x,y:Alph*//(x R y))(x,y:Alph*//(x R y)))*
12. u: (x,y:Alph*//(x R y))(x,y:Alph*//(x R y))
13. v: ((x,y:Alph*//(x R y))(x,y:Alph*//(x R y)))*
14. Dec(p:((x,y:Alph*//(x R y))(x,y:Alph*//(x R y))). (p/p1,p2.(g(p1)) = (g(p2))) = false & mem_f((x,y:Alph*//(x R y))(x,y:Alph*//(x R y));p;v))
15. (u/u1,u2.(g(u1)) = (g(u2))) = false

Dec(p:((x,y:Alph*//(x R y))(x,y:Alph*//(x R y))). (p/p1,p2.(g(p1)) = (g(p2))) = false & u = p mem_f((x,y:Alph*//(x R y))(x,y:Alph*//(x R y));p;v))
By: Analyze -2
Generated subgoals:

114. p:((x,y:Alph*//(x R y))(x,y:Alph*//(x R y))). (p/p1,p2.(g(p1)) = (g(p2))) = false & mem_f((x,y:Alph*//(x R y))(x,y:Alph*//(x R y));p;v)
15. (u/u1,u2.(g(u1)) = (g(u2))) = false
Dec(p:((x,y:Alph*//(x R y))(x,y:Alph*//(x R y))). (p/p1,p2.(g(p1)) = (g(p2))) = false & u = p mem_f((x,y:Alph*//(x R y))(x,y:Alph*//(x R y));p;v))
214. (p:((x,y:Alph*//(x R y))(x,y:Alph*//(x R y))). (p/p1,p2.(g(p1)) = (g(p2))) = false & mem_f((x,y:Alph*//(x R y))(x,y:Alph*//(x R y));p;v))
15. (u/u1,u2.(g(u1)) = (g(u2))) = false
Dec(p:((x,y:Alph*//(x R y))(x,y:Alph*//(x R y))). (p/p1,p2.(g(p1)) = (g(p2))) = false & u = p mem_f((x,y:Alph*//(x R y))(x,y:Alph*//(x R y));p;v))

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