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Proof step 18 from proof okarrays-put (previous step)

sk .fs = mkfs(class, ty, fieldvar), oktype(val, ty, st), goodfieldandtype(r0, sk, st), ∀ sk, class, ty, fieldvar, val, st, r0, r. sk .fs = mkfs(class, ty, fieldvar) ∧ oktype(val, ty, st) ∧ goodfieldandtype(r0, sk, st) → sk = _type ∨ sk = _length ∨ (okarrays(r, fis0, st[r0 -- sk, val]) ↔ okarrays(r, fis0, st)) ∨ sk ∈ fis0 ⊦ sk = _type, sk = _length, okarrays(r, fv ' + fis0, st[r0 -- sk, val]) ↔ okarrays(r, fv ' + fis0, st), sk ∈ fv ', sk ∈ fis0

User applied rule structural induction

And obtained the following new goals

Proof step 17:
sk .fs = mkfs(class, ty, fieldvar), oktype(val, ty, st), goodfieldandtype(r0, sk, st), ∀ sk, class, ty, fieldvar, val, st, r0, r. sk .fs = mkfs(class, ty, fieldvar) ∧ oktype(val, ty, st) ∧ goodfieldandtype(r0, sk, st) → sk = _type ∨ sk = _length ∨ (okarrays(r, fis0, st[r0 -- sk, val]) ↔ okarrays(r, fis0, st)) ∨ sk ∈ fis0 ⊦ sk = _type, sk = _length, okarrays(r, (sk0 × val0) ' + fis0, st[r0 -- sk, val]) ↔ okarrays(r, (sk0 × val0) ' + fis0, st), sk ∈ (sk0 × val0) ', sk ∈ fis0

Rule argument

[VARWITHFMAVARSARG : fv, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : fieldvalue generated by ×;])]]