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Proof step 33 from proof addarray-identity (previous step)

st[r -- _type] .type = mkarraytype(ty), 0 ≤ sk .index, sk .index < n→i(# getarray(r, st)), is_indexkey(sk), is_array(r, st) ⊦ getarray(r, st) = [], (r -- sk ∈ addarray(r, ty, getarray(r, st), st) → r -- sk ∈ st) ∧ (addarray(r, ty, getarray(r, st), st)[r -- sk]) = st[r -- sk]

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 32:
sk = i ', st[r -- _type] .type = mkarraytype(ty), 0 ≤ i, i < n→i(# getarray(r, st)), is_indexkey(sk), is_array(r, st) ⊦ getarray(r, st) = [], (r -- sk ∈ addarray(r, ty, getarray(r, st), st) → r -- sk ∈ st) ∧ (addarray(r, ty, getarray(r, st), st)[r -- sk]) = st[r -- sk]

Rule argument

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

Additional information

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