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Proof step 8 from proof add-in-other (previous step)

r0 -- sk ∈ addarray(r0, ty, vals, st), is_indexkey(sk) ∧ (sk .index < 0 ∨ n→i(# vals) ≤ sk .index) ∨ is_fskey(sk) ∧ sk ≠ _length ∧ sk ≠ _type ⊦ r0 -- sk ∈ st

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ is_fskey(sk) ∧ sk ≠ _length ∧ sk ≠ _type → (r -- sk ∈ addarray(r, ty, vals, st) ↔ r -- sk ∈ st)
Proof step 7:
¬ (is_fskey(sk) ∧ sk ≠ _length ∧ sk ≠ _type), r0 -- sk ∈ addarray(r0, ty, vals, st), is_indexkey(sk) ∧ (sk .index < 0 ∨ n→i(# vals) ≤ sk .index) ∨ is_fskey(sk) ∧ sk ≠ _length ∧ sk ≠ _type ⊦ r0 -- sk ∈ st

Rule argument

[crewrite-arg: add-in-fskey , F , [st, vals, ty, sk, r] → [st, vals, ty, sk, r0] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, vals, ty, sk, r0)]]