Nuprl - Pf reach_lemma 1 2 2 1 1 2 1 2 1

PrintForm Definitions det automata Sections AutomataTheory Doc

1. Alph: Type
2. S: ActionSet(Alph)
3. si: S.car
4. nn:
5. f: nnAlph
6. g: Alphnn
7. Fin(S.car)
8. InvFuns(nn; Alph; f; g)
9. n:
10. 0 < n
11. RL: {y:{x:(S.car*)| 0 < ||x|| & ||x||n-1+1 }| y[(||y||-1)] = si }
12. ||RL|| = n-1+1
13. i:||RL||, j:i. RL[i] = RL[j]
14. s:S.car. mem_f(S.car;s;RL) (w:Alph*. (S:wsi) = s)
15. k:. knn (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)))
16. RLa: S.car*
17. 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)
18. a:Alph. g(a) < nn mem_f(S.car;S.act(a,hd(RL));RL) mem_f(S.car;S.act(a,hd(RL));RLa)
19. s:S.car. mem_f(S.car;s;RLa) (w:Alph*. (S:wsi) = s)
20. La': S.car*
21. t:S.car. mem_f(S.car;t;RLa) mem_f(S.car;t;RL) mem_f(S.car;t;La')
22. t:S.car. mem_f(S.car;t;La') mem_f(S.car;t;RLa)
23. La' = nil
24. s: S.car
25. w:Alph*. (S:wsi) = s

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

By: Thin -1 THEN RecUnfold `maction` 0 THEN Analyze 0 THEN ListInd -1 THEN Reduce 0

Generated subgoals:

1 25. w: Alph*
mem_f(S.car;si;RL)

2 25. w: Alph*
26. u: Alph
27. v: Alph*
28. mem_f(S.car;if null(v) si else S.act(hd(v),(S:tl(v)si)) fi;RL)
mem_f(S.car;S.act(u,(S:vsi));RL)

About:

1	25. `w:` `Alph*` `mem_f(S.car;si;RL)`
2	25. `w:` `Alph` 26. `u:` `Alph` 27. `v:` `Alph` 28. `mem_f(S.car;if null(v) si else S.act(hd(v),(S:tl(v)si)) fi;RL)` `mem_f(S.car;S.act(u,(S:vsi));RL)`