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At: reach lemma 1 2 2 1 1 2 1
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

RL:{y:{x:(S.car*)| 0 < ||x|| & ||x||n+1 }| y[(||y||-1)] = si }. (s:S.car. (w:Alph*. (S:wsi) = s) mem_f(S.car;s;RL)) ||RL|| = n+1 & (i:||RL||, j:i. RL[i] = RL[j]) & (s:S.car. mem_f(S.car;s;RL) (w:Alph*. (S:wsi) = s)) & (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))))
By:
InstConcl [RL]
THEN
Sel 1 (Analyze 0)
THEN
GenRepD
Generated subgoals:

111. RL: S.car*
12. 0 < ||RL||
13. ||RL||n-1+1
14. RL[(||RL||-1)] = si
15. ||RL|| = n-1+1
16. i:||RL||, j:i. RL[i] = RL[j]
17. s:S.car. mem_f(S.car;s;RL) (w:Alph*. (S:wsi) = s)
18. 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)))
19. RLa: S.car*
20. 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)
21. 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)
22. s:S.car. mem_f(S.car;s;RLa) (w:Alph*. (S:wsi) = s)
23. La': S.car*
24. t:S.car. mem_f(S.car;t;RLa) mem_f(S.car;t;RL) mem_f(S.car;t;La')
25. t:S.car. mem_f(S.car;t;La') mem_f(S.car;t;RLa)
26. La' = nil
27. y: {x:(S.car*)| 0 < ||x|| & ||x||n+1 }
0||y||-1
224. s: S.car
25. w:Alph*. (S:wsi) = s
mem_f(S.car;s;RL)
324. s: S.car
25. mem_f(S.car;s;RL)
w:Alph*. (S:wsi) = s
424. R1: {y:{x:(S.car*)| 0 < ||x|| & ||x||n+1 }| y[(||y||-1)] = si }
25. k:
26. knn
27. R2: S.car*
28. a: Alph
29. g(a) < k
||R1||1
524. R1: {y:{x:(S.car*)| 0 < ||x|| & ||x||n+1 }| y[(||y||-1)] = si }
25. k:
26. knn
27. R2: S.car*
28. a: Alph
29. g(a) < k
||R1||1

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