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Proof step 6 from proof add-refs (previous step)

∀ st, ty, r, vals0. # vals0 < # vals → (true → addarray(r, ty, vals0, st) .refs = st .refs ++ r) ⊦ vals = [], addarray(r, ty, vals .butlast, st) .refs ++ r = st .refs ++ r

User applied rule apply induction

And closed the goal!

Rule argument

[substlist-arg: [st, ty, r, vals0] → [st, ty, r, vals .butlast]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ rset ++ r ++ r = rset ++ r], [CSIMPSEQ : ⊦ vals ≠ [] → # vals .butlast = # vals - 1], [CSIMPSEQ : ⊦ # vals = 0 ↔ vals = []], [CSIMPSEQ : ⊦ m < 1 ↔ m = 0], [CSIMPSEQ : ⊦ ¬ m ≤ n ↔ n < m], [CSIMPSEQ : n0 ≤ n ⊦ n - n0 < m ↔ n < m + n0], [CSIMPSEQ : ⊦ m < n + 1 ↔ ¬ n < m], [CSIMPSEQ : ⊦ ¬ n < n], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m])], [EXTRATERMS : (st, ty, r, vals .butlast)]]