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Proof step 11 from proof validfield-superset (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ goodfieldandtype(r, sk, st) ↔ is_fskey(sk) ∧ r -- sk ∈ st ∧ okval(st[r -- sk], sk .fs .type)
Proof step 10:
r -- mkfs(class, ty, fieldvar) ' ∈ st, r ∈ st, type∃(str, ty), st ⊆ st0, okval(st[r -- mkfs(class, ty, fieldvar) '], ty), is_reftype(ty) → validrefval(str, st[r -- mkfs(class, ty, fieldvar) '], ty, st) ⊦ ty = void_type, is_fskey(mkfs(class, ty, fieldvar) ') ∧ r -- mkfs(class, ty, fieldvar) ' ∈ st0 ∧ okval(st0[r -- mkfs(class, ty, fieldvar) '], mkfs(class, ty, fieldvar) ' .fs .type) ∧ (is_reftype(ty) → validrefval(str, st0[r -- mkfs(class, ty, fieldvar) '], 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] → [st0, mkfs(class, ty, fieldvar) ', r] ,F ,okfuns , ,good-field-def ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st0, mkfs(class, ty, fieldvar) ', r)]]