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Proof step 3 from proof in-init-01 (previous step)

⊦ r = r0, r -- sk ∈ addarray(r0, ty, vals, st) ↔ r -- sk ∈ 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 -- sk ∈ addarray(r0, vals, j, st) ↔ r -- sk ∈ st)

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r ≠ r0 → ( r -- sk ∈ st[r0 -- sk0, val] ↔ r -- sk ∈ st)])], [EXTRATERMS : (st, vals, ty, r0)]]