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Proof step 6 from proof okarray-update (previous step)

∀ r, r0, ty, i, st. r = r0 ∨ (okarray(refval(r), ty, i, update(r0, fis0, st)) ↔ okarray(refval(r), ty, i, st)) ⊦ r = r0, okarray(refval(r), ty, i, update(r0, fis0, st)[r0 -- sk, val]) ↔ okarray(refval(r), ty, i, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ refval(rk .ref) ≠ val → (okarray(val, ty, i, st[rk, val0]) ↔ okarray(val, ty, i, st))
Proof step 5:
refval((r0 -- sk) .ref) ≠ refval(r), ∀ r, r0, ty, i, st. r = r0 ∨ (okarray(refval(r), ty, i, update(r0, fis0, st)) ↔ okarray(refval(r), ty, i, st)) ⊦ r = r0, okarray(refval(r), ty, i, update(r0, fis0, st)) ↔ okarray(refval(r), ty, i, st)

Rule argument

[crewrite-arg: okarray-put-07 , F , [val0, rk, st, i, ty, val] → [val, r0 -- sk, update(r0, fis0, st), i, ty, refval(r)] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (r -- sk) .ref = r], [CSIMPSEQ : ⊦ refval(r) = refval(r0) ↔ r = r0])], [EXTRATERMS : (val, r0 -- sk, update(r0, fis0, st), i, ty, refval(r))]]