Alph:Type, S:ActionSet(Alph), si:S.car, nn:, f:(nnAlph), g:(Alphnn). Fin(S.car) InvFuns(nn; Alph; f; g) (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)))))

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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))))

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