PrintForm Definitions myhill nerode Sections AutomataTheory Doc

At: total back listify 1 1 2 2 2 2
1. Alph: Type
2. S: ActionSet(Alph)
3. sL: S.car*
4. Fin(Alph)
5. Fin(S.car)
6. n:
7. 0 < n
8. TBL: S.car*
9. ||TBL|| = n-1
10. i:||TBL||, j:i. TBL[i] = TBL[j]
11. s:S.car. mem_f(S.car;s;TBL) (w:Alph*. mem_f(S.car;(S:ws);sL))
12. AL: S.car*
13. u: S.car
14. v: S.car*
15. (s:S.car. mem_f(S.car;s;v) (w:Alph*. mem_f(S.car;(S:ws);sL))) (s:S.car. mem_f(S.car;s;sL) mem_f(S.car;s;TBL) mem_f(S.car;s;v)) (s:S.car, a:Alph. mem_f(S.car;S.act(a,s);TBL) mem_f(S.car;s;TBL) mem_f(S.car;s;v)) (TBL:S.car*. (s:S.car. mem_f(S.car;s;TBL) (w:Alph*. mem_f(S.car;(S:ws);sL))) ||TBL|| = n & (i:||TBL||, j:i. TBL[i] = TBL[j]) & (s:S.car. mem_f(S.car;s;TBL) (w:Alph*. mem_f(S.car;(S:ws);sL))) & (AL:S.car*. (s:S.car. mem_f(S.car;s;AL) (w:Alph*. mem_f(S.car;(S:ws);sL))) & (s:S.car. mem_f(S.car;s;sL) mem_f(S.car;s;TBL) mem_f(S.car;s;AL)) & (s:S.car, a:Alph. mem_f(S.car;S.act(a,s);TBL) mem_f(S.car;s;TBL) mem_f(S.car;s;AL))))
16. s:S.car. u = s mem_f(S.car;s;v) (w:Alph*. mem_f(S.car;(S:ws);sL))
17. s:S.car. mem_f(S.car;s;sL) mem_f(S.car;s;TBL) u = s mem_f(S.car;s;v)
18. s:S.car, a:Alph. mem_f(S.car;S.act(a,s);TBL) mem_f(S.car;s;TBL) u = s mem_f(S.car;s;v)
19. mem_f(S.car;u;TBL)

TBL:S.car*. (s:S.car. mem_f(S.car;s;TBL) (w:Alph*. mem_f(S.car;(S:ws);sL))) ||TBL|| = n & (i:||TBL||, j:i. TBL[i] = TBL[j]) & (s:S.car. mem_f(S.car;s;TBL) (w:Alph*. mem_f(S.car;(S:ws);sL))) & (AL:S.car*. (s:S.car. mem_f(S.car;s;AL) (w:Alph*. mem_f(S.car;(S:ws);sL))) & (s:S.car. mem_f(S.car;s;sL) mem_f(S.car;s;TBL) mem_f(S.car;s;AL)) & (s:S.car, a:Alph. mem_f(S.car;S.act(a,s);TBL) mem_f(S.car;s;TBL) mem_f(S.car;s;AL)))
By:
Thin 15
THEN
Thin 12
THEN
InstConcl [u.TBL]
THEN
Sel 2 (Analyze 0)
THEN
Reduce 0
Generated subgoals:

112. u: S.car
13. v: S.car*
14. s:S.car. u = s mem_f(S.car;s;v) (w:Alph*. mem_f(S.car;(S:ws);sL))
15. s:S.car. mem_f(S.car;s;sL) mem_f(S.car;s;TBL) u = s mem_f(S.car;s;v)
16. s:S.car, a:Alph. mem_f(S.car;S.act(a,s);TBL) mem_f(S.car;s;TBL) u = s mem_f(S.car;s;v)
17. mem_f(S.car;u;TBL)
18. i: (||TBL||+1)
19. j: i
(u.TBL)[i] = (u.TBL)[j]
212. u: S.car
13. v: S.car*
14. s:S.car. u = s mem_f(S.car;s;v) (w:Alph*. mem_f(S.car;(S:ws);sL))
15. s:S.car. mem_f(S.car;s;sL) mem_f(S.car;s;TBL) u = s mem_f(S.car;s;v)
16. s:S.car, a:Alph. mem_f(S.car;S.act(a,s);TBL) mem_f(S.car;s;TBL) u = s mem_f(S.car;s;v)
17. mem_f(S.car;u;TBL)
18. s: S.car
19. u = s mem_f(S.car;s;TBL)
w:Alph*. mem_f(S.car;(S:ws);sL)
312. u: S.car
13. v: S.car*
14. s:S.car. u = s mem_f(S.car;s;v) (w:Alph*. mem_f(S.car;(S:ws);sL))
15. s:S.car. mem_f(S.car;s;sL) mem_f(S.car;s;TBL) u = s mem_f(S.car;s;v)
16. s:S.car, a:Alph. mem_f(S.car;S.act(a,s);TBL) mem_f(S.car;s;TBL) u = s mem_f(S.car;s;v)
17. mem_f(S.car;u;TBL)
AL:S.car*. (s:S.car. mem_f(S.car;s;AL) (w:Alph*. mem_f(S.car;(S:ws);sL))) & (s:S.car. mem_f(S.car;s;sL) u = s mem_f(S.car;s;TBL) mem_f(S.car;s;AL)) & (s:S.car, a:Alph. u = S.act(a,s) mem_f(S.car;S.act(a,s);TBL) u = s mem_f(S.car;s;TBL) mem_f(S.car;s;AL))

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existslistorallandequalnatural_number
impliesapplyconsuniverseintless_thansubtract