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Proof step 15 from proof in-add (previous step)

# vals = m + 1, ∀ st, ty, j, r, vals0. # vals0 < m + 1 → (true → (r -- j ' ∈ addarray(r, ty, vals0, st) ↔ ¬ j < 0 ∧ ¬ n→i(# vals0) ≤ j ∨ r -- j ' ∈ st)) ⊦ vals = [], r -- j ' ∈ (addarray(r, ty, vals .butlast, st)[r -- n→i(m) ', vals .last]) ↔ r -- j ' ∈ st ∨ ¬ j < 0 ∧ ¬ n→i(m) < j

User applied rule insert elim lemma

And obtained the following new goals

Proof step 14:
vals = vals1 + val ', # vals = m + 1, ∀ st, ty, j, r, vals0. # vals0 < m + 1 → (true → (r -- j ' ∈ addarray(r, ty, vals0, st) ↔ ¬ j < 0 ∧ ¬ n→i(# vals0) ≤ j ∨ r -- j ' ∈ st)) ⊦ vals = [], r -- j ' ∈ (addarray(r, ty, vals1, st)[r -- n→i(m) ', val]) ↔ r -- j ' ∈ st ∨ ¬ j < 0 ∧ ¬ n→i(m) < j

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)]]