Nuprl - Pf reach_aux 1 1 1 1 2

PrintForm Definitions det automata Sections AutomataTheory Doc

1. Alph: Type
2. S: ActionSet(Alph)
3. si: S.car
4. Fin(S.car)
5. n:
6. f: nAlph
7. g: Alphn
8. InvFuns(n; Alph; f; g)
9. n1:
10. f1: n1S.car
11. g1: S.carn1
12. InvFuns(n1; S.car; f1; g1)
13. RL: {y:{x:(S.car*)| 0 < ||x|| & ||x||n1+1 }| y[(||y||-1)] = si }
14. ||RL|| = n1+1
15. i:||RL||, j:i. RL[i] = RL[j]
16. s:S.car. mem_f(S.car;s;RL) (w:Alph*. (S:wsi) = s)
17. k:. kn (RLa:S.car*. (i:{1..||RL||}, a:Alph. mem_f(S.car;S.act(a,RL[i]);RL) mem_f(S.car;S.act(a,RL[i]);RLa)) & (a:Alph. g(a) < k mem_f(S.car;S.act(a,hd(RL));RL) mem_f(S.car;S.act(a,hd(RL));RLa)) & (s:S.car. mem_f(S.car;s;RLa) (w:Alph*. (S:wsi) = s)))

RL:S.car*. s:S.car. (w:Alph*. (S:wsi) = s) mem_f(S.car;s;RL)

By: Thin -1 THEN Inst Thm* n:{1...}, f:((n+1)n). i:(n+1), j:i. f(i) = f(j) [n1;x.g1(RL[x])] THEN ExRepD

Generated subgoals:

1 1n1

2 17. i: (n1+1)
18. j: i
19. (x.g1(RL[x]))(i) = (x.g1(RL[x]))(j) n1
RL:S.car*. s:S.car. (w:Alph*. (S:wsi) = s) mem_f(S.car;s;RL)

About:

1	`1n1`
2	17. `i:` `(n1+1)` 18. `j:` `i` 19. `(x.g1(RL[x]))(i) = (x.g1(RL[x]))(j) n1` `RL:S.car. s:S.car. (w:Alph. (S:wsi) = s) mem_f(S.car;s;RL)`