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Proof step 3 from proof in-1init (previous step)

⊦ r = r0, r ∈ addarray(r0, ty0, vals, st) ↔ r ∈ st

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ addarray(r, ty, vals, st) = addarray(r, vals, 0, st[r -- _type, typeval(mkarraytype(ty))][r -- _length, intval(n→i(# vals))])
Proof step 2:
⊦ r ≠ r0 → (r ∈ addarray(r0, vals, j, st) ↔ r ∈ st)

Rule argument

[crewrite-arg: addarrayinit-def , F , [st, vals, ty, r] → [st, vals, ty0, r0] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r ∈ st[r0 -- sk, val] ↔ r = r0 ∨ r ∈ st])], [EXTRATERMS : (st, vals, ty0, r0)]]