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Proof step 11 from proof add-in-fskey (previous step)

is_fskey(sk), r -- sk ∈ addarray(r, ty, vals1, st), ∀ st, ty, sk, r, vals0. # vals0 < # (vals1 + val ') → (r -- sk ∈ addarray(r, ty, vals0, st) ∧ is_fskey(sk) → sk = _length ∨ sk = _type ∨ r -- sk ∈ st) ⊦ sk = _type, sk = _length, r -- sk ∈ st

User applied rule apply induction

And closed the goal!

Rule argument

[substlist-arg: [st, ty, sk, r, vals0] → [st, ty, sk, r, vals1]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_indexkey(sk) → ¬ is_fskey(sk)], [CSIMPSEQ : ⊦ ¬ is_fskey(sk) ↔ is_indexkey(sk)], [CSIMPSEQ : ⊦ # (vals + vals0) = # vals + # vals0], [CSIMPSEQ : ⊦ # val ' = 0 +1], [CSIMPSEQ : ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1], [CSIMPSEQ : ⊦ m < n + 1 ↔ ¬ n < m], [CSIMPSEQ : ⊦ ¬ n < n], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m])], [EXTRATERMS : (st, ty, sk, r, vals1)]]