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Proof step 15 from proof validfield-superset (previous step)

sk .fs = mkfs(class, ty, fieldvar), goodfieldandtype(r, sk, st), st ⊆ st0, type∃(str, ty), is_reftype(ty) → validrefval(str, st[r -- sk], ty, st) ⊦ ty = void_type, goodfieldandtype(r, sk, st0) ∧ (is_reftype(ty) → validrefval(str, st0[r -- sk], ty, st0))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ goodfieldandtype(r, sk, st) ↔ is_fskey(sk) ∧ r -- sk ∈ st ∧ okval(st[r -- sk], sk .fs .type)
Proof step 14:
sk .fs = mkfs(class, ty, fieldvar), is_fskey(sk) ∧ r -- sk ∈ st ∧ okval(st[r -- sk], sk .fs .type), st ⊆ st0, type∃(str, ty), is_reftype(ty) → validrefval(str, st[r -- sk], ty, st) ⊦ ty = void_type, goodfieldandtype(r, sk, st0) ∧ (is_reftype(ty) → validrefval(str, st0[r -- sk], ty, st0))

Rule argument

[speclemmaarg: , goodfieldandtype(r, sk, st) ↔ is_fskey(sk) ∧ r -- sk ∈ st ∧ okval(st[r -- sk], sk .fs .type) ,[st, sk, r] → [st, sk, r] ,F ,okfuns , ,good-field-def ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, sk, r)]]