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At: reach lemma 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:

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: NatInd 9
Generated subgoals:

1 RL:{y:{x:(S.car*)| 0 < ||x|| & ||x||0+1 }| y[(||y||-1)] = si }. (s:S.car. (w:Alph*. (S:wsi) = s) mem_f(S.car;s;RL)) ||RL|| = 0+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))))
29. n:
10. 0 < n
11. RL:{y:{x:(S.car*)| 0 < ||x|| & ||x||n-1+1 }| y[(||y||-1)] = si }. (s:S.car. (w:Alph*. (S:wsi) = s) mem_f(S.car;s;RL)) ||RL|| = n-1+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))))
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))))

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