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Proof step 13 from proof add-in-fskey (previous step)

r -- sk ∈ addarray(r, ty, vals .butlast, st), is_fskey(sk), ∀ st, ty, sk, r, vals0. # vals0 < # vals → (r -- sk ∈ addarray(r, ty, vals0, st) ∧ is_fskey(sk) → sk = _length ∨ sk = _type ∨ r -- sk ∈ st) ⊦ vals = [], sk = _length, sk = _type, r -- sk ∈ st

User applied rule insert elim lemma

And obtained the following new goals

Proof step 12:
vals = vals1 + val ', r -- sk ∈ addarray(r, ty, vals1, st), is_fskey(sk), ∀ st, ty, sk, r, vals0. # vals0 < # vals → (r -- sk ∈ addarray(r, ty, vals0, st) ∧ is_fskey(sk) → sk = _length ∨ sk = _type ∨ r -- sk ∈ st) ⊦ vals = [], sk = _length, sk = _type, r -- sk ∈ st

Rule argument

[speclemmaarg: vals ≠ [] ,val = vals .last ∧ vals0 = vals .butlast ↔ vals = vals0 + val ' ,[vals, val, vals0] → [vals, val, vals1] ,T ,list-last ,javavalues ,last-elim ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : vals ≠ [] ⊦ val = vals .last ∧ vals0 = vals .butlast ↔ vals = vals0 + val '])], [EXTRATERMS : (vals, val, vals1)]]