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Proof step 145 from proof putarray-addarray-01 (previous step)

0 ≤ n→i(# vals) + i, 0 ≤ j, 0 ≤ i, i ≤ j, j ≤ n→i(# vals) + i, is_indexkey(sk), r -- sk ∈ putArray(vals, r, i, addarray(r, ty, j, st)), r ∈ putArray(vals, r, i, addarray(r, ty, j, st)), sk .index < 0 ∨ i + n→i(# vals) ≤ sk .index ⊦ sk = _length, sk = _type, r -- sk ∈ st

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 144:
sk = i0 ', 0 ≤ n→i(# vals) + i, 0 ≤ j, 0 ≤ i, i ≤ j, j ≤ n→i(# vals) + i, is_indexkey(sk), r -- sk ∈ putArray(vals, r, i, addarray(r, ty, j, st)), r ∈ putArray(vals, r, i, addarray(r, ty, j, st)), i0 < 0 ∨ i + n→i(# vals) ≤ i0 ⊦ sk = _length, sk = _type, r -- sk ∈ st

Rule argument

[speclemmaarg: ,is_indexkey(sk) → (i = sk .index ↔ sk = i ') ,[sk, i] → [sk, i0] ,T ,storekey , ,elim-04 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_indexkey(sk) → (i = sk .index ↔ sk = i ')])], [EXTRATERMS : (sk, i0)]]