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Proof step 10 from proof putarray-add-same (previous step)

0 ≤ sk .index, sk .index < n→i(# vals), is_indexkey(sk) ⊦ sk = _length, sk = _type, vals = [], r0 -- sk ∈ addarray(r0, ty, vals, st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 9:
⊦ r -- j ' ∈ addarray(r, ty, vals, st) ↔ r -- j ' ∈ st ∨ 0 ≤ j ∧ j < n→i(# vals)

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ _length ≠ i '], [CSIMPSEQ : ⊦ _type ≠ i '], [CSIMPSEQ : ⊦ is_indexkey(i ')], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)], [CSIMPELIM : ⊦ is_indexkey(sk) → (i = sk .index ↔ sk = i ')])], [EXTRATERMS : (sk, i)]]