Nuprl - Pf reach_lemma 1 2 2 1 1 1 2

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'||1 mem_f(S.car;hd(La');RL)
24. ||La'||1

(s:S.car. (w:Alph*. (S:wsi) = s) mem_f(S.car;s;hd(La').RL)) ||hd(La').RL|| = n+1 & (i:||hd(La').RL||, j:i. (hd(La').RL)[i] = (hd(La').RL)[j]) & (s:S.car. mem_f(S.car;s;hd(La').RL) (w:Alph*. (S:wsi) = s)) & (k:. knn (RLa:S.car*. (i:{1..||hd(La').RL||}, a:Alph. mem_f(S.car;S.act(a,(hd(La').RL)[i]);hd(La').RL) mem_f(S.car;S.act(a,(hd(La').RL)[i]);RLa)) & (a:Alph. g(a) < k mem_f(S.car;S.act(a,hd((hd(La').RL)));hd(La').RL) mem_f(S.car;S.act(a,hd((hd(La').RL)));RLa)) & (s:S.car. mem_f(S.car;s;RLa) (w:Alph*. (S:wsi) = s))))

By: Reduce 0 THEN Sel 2 (Analyze 0)

Generated subgoals:

1 25. i: (||RL||+1)
26. j: i
(hd(La').RL)[i] = (hd(La').RL)[j]

2 25. s: S.car
26. hd(La') = s mem_f(S.car;s;RL)
w:Alph*. (S:wsi) = s

3 25. k:
26. knn
RLa:S.car*. (i:{1..(||RL||+1)}, a:Alph. hd(La') = S.act(a,(hd(La').RL)[i]) mem_f(S.car;S.act(a,(hd(La').RL)[i]);RL) mem_f(S.car;S.act(a,(hd(La').RL)[i]);RLa)) & (a:Alph. g(a) < k hd(La') = S.act(a,hd(La')) mem_f(S.car;S.act(a,hd(La'));RL) mem_f(S.car;S.act(a,hd(La'));RLa)) & (s:S.car. mem_f(S.car;s;RLa) (w:Alph*. (S:wsi) = s))

About:

1	25. `i:` `(\|\|RL\|\|+1)` 26. `j:` `i` `(hd(La').RL)[i] = (hd(La').RL)[j]`
2	25. `s:` `S.car` 26. `hd(La') = s mem_f(S.car;s;RL)` `w:Alph*. (S:wsi) = s`
3	25. `k:` 26. `knn` `RLa:S.car. (i:{1..(\|\|RL\|\|+1)}, a:Alph. hd(La') = S.act(a,(hd(La').RL)[i]) mem_f(S.car;S.act(a,(hd(La').RL)[i]);RL) mem_f(S.car;S.act(a,(hd(La').RL)[i]);RLa)) & (a:Alph. g(a) < k hd(La') = S.act(a,hd(La')) mem_f(S.car;S.act(a,hd(La'));RL) mem_f(S.car;S.act(a,hd(La'));RLa)) & (s:S.car. mem_f(S.car;s;RLa) (w:Alph. (S:wsi) = s))`