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Proof step 17 from proof validrefnotnull-union-at-right (previous step)

st0[r -- _type] = typeval(mkclasstype(class0)), class+∃(str, class0), r ∈ st0, mkfs(class1, ty, fieldvar) ' ∈ instfields(class), class0 ≤ class, r -- _type ∈ st0, goodfieldsandtypes(r, instfields(class0), st0) ⊦ r = jvmref, st[r -- mkfs(class1, ty, fieldvar) '] = noval, r -- mkfs(class1, ty, fieldvar) ' ∈ st0, is_abstract(class0), (is_reftype(ty) ∨ ty = abstract_type) ∧ noval .refval ≠ jvmref

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ goodfieldsandtypes(r, sks, st) ↔ (∀ sk. sk ∈ sks → goodfieldandtype(r, sk, st))
Proof step 16:
st0[r -- _type] = typeval(mkclasstype(class0)), class+∃(str, class0), r ∈ st0, mkfs(class1, ty, fieldvar) ' ∈ instfields(class), class0 ≤ class, r -- _type ∈ st0, ∀ sk. sk ∈ instfields(class0) → goodfieldandtype(r, sk, st0) ⊦ r = jvmref, st[r -- mkfs(class1, ty, fieldvar) '] = noval, r -- mkfs(class1, ty, fieldvar) ' ∈ st0, is_abstract(class0), (is_reftype(ty) ∨ ty = abstract_type) ∧ noval .refval ≠ jvmref

Rule argument

[speclemmaarg: , goodfieldsandtypes(r, sks, st) ↔ (∀ sk. sk ∈ sks → goodfieldandtype(r, sk, st)) ,[st, sks, r] → [st0, instfields(class0), r] ,F ,okfuns , ,gfts-all ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st0, instfields(class0), r)]]