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Proof step 80 from proof putarray-addarray-one (previous step)

is_fskey(sk), is_reftype(ty), r -- sk ∈ addarray(r, ty, n→i(# vals) + 1, st) ∨ is_indexkey(sk) ∧ 0 < sk .index ∧ sk .index ≤ n→i(# vals) ⊦ sk = _type, sk = _length, r -- sk ∈ st

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 78:
⊦ is_fskey(sk) ∧ sk ≠ _length ∧ sk ≠ _type → (r -- sk ∈ addarray(r, ty, i, st) ↔ r -- sk ∈ st)
Proof step 79:
⊦ is_fskey(sk) ∧ sk ≠ _length ∧ sk ≠ _type → (r -- sk ∈ addarray(r, ty, i, st) ↔ r -- sk ∈ st)

Rule argument

[crewrite-arg: in-1dim-fskey , F , [st, i, ty, sk, r] → [st, n→i(# vals) + 1, ty, sk, r] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_indexkey(sk) → ¬ is_fskey(sk)])], [EXTRATERMS : (st, n→i(# vals) + 1, ty, sk, r)]]