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Proof step 7 from proof gengfts (previous step)

sk .fs = mkfs(class, ty, fieldvar), oktype(val, ty, st), goodfieldandtype(r, sk, st), ∀ sk, class, ty, fieldvar, val, st, r, r0. sk .fs = mkfs(class, ty, fieldvar) ∧ oktype(val, ty, st) ∧ goodfieldandtype(r, sk, st) → sk = _type ∨ (goodfieldsandtypes(r0, sks0, st[r -- sk, val]) ↔ goodfieldsandtypes(r0, sks0, st)) ⊦ sk = _type, goodfieldandtype(r0, sk0, st[r -- sk, val]) ∧ goodfieldsandtypes(r0, sks0, st[r -- sk, val]) ↔ goodfieldandtype(r0, sk0, st) ∧ goodfieldsandtypes(r0, sks0, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ sk ≠ _type ∧ goodfieldandtype(r, sk, st) ∧ oktype(val, sk .fs .type, st) → (goodfieldandtype(r0, sk0, st[r -- sk, val]) ↔ goodfieldandtype(r0, sk0, st))
Proof step 6:
sk ≠ _type ∧ goodfieldandtype(r, sk, st) ∧ oktype(val, sk .fs .type, st), sk .fs = mkfs(class, ty, fieldvar), oktype(val, ty, st), goodfieldandtype(r, sk, st), ∀ sk, class, ty, fieldvar, val, st, r, r0. sk .fs = mkfs(class, ty, fieldvar) ∧ oktype(val, ty, st) ∧ goodfieldandtype(r, sk, st) → sk = _type ∨ (goodfieldsandtypes(r0, sks0, st[r -- sk, val]) ↔ goodfieldsandtypes(r0, sks0, st)) ⊦ sk = _type, goodfieldandtype(r0, sk0, st) ∧ goodfieldsandtypes(r0, sks0, st[r -- sk, val]) ↔ goodfieldandtype(r0, sk0, st) ∧ goodfieldsandtypes(r0, sks0, st)

Rule argument

[crewrite-arg: gengft , F , [val, sk, r, st, sk0, r0] → [val, sk, r, st, sk0, r0] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ mkfs(class, ty, fieldvar) .type = ty])], [EXTRATERMS : (val, sk, r, st, sk0, r0)]]