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Proof step 18 from proof resetcnt-mod-cnt (previous step)

P[n] = pe(m, m0, m1), n < # P ⊦ resetcnt(P[n, pe(m, m0, m2)]) = resetcnt(P), P = []

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 17:
∀ n, m, m0, m1, m2. P0[n] = pe(m, m0, m1) ∧ n < # P0 → resetcnt(P0[n, pe(m, m0, m2)]) = resetcnt(P0) ∨ P0 = [], (p + P0)[n] = pe(m, m0, m1), n < #(p + P0) ⊦ resetcnt((p + P0)[n, pe(m, m0, m2)]) = resetcnt(p + P0), p + P0 = []

Rule argument

term:P

Additional information

[Concretesimprules((Csimpgen(partition freely generated by [], +;)))]