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Proof step 19 from proof isobj-subset (previous step)

st[r -- _type] = typeval(mkclasstype(class)), st1[r -- _type] = typeval(mkclasstype(class)), r ∈ st1, r ∈ st, r -- _type ∈ st1, ∀ sk. sk ∈ instfields(class) → goodfieldandtype(r, sk, st), r -- _type ∈ st, ∀ rk. rk ∈ st → rk ∈ st1 ∧ st[rk] = st1[rk] ⊦ r = jvmref, goodfieldsandtypes(r, instfields(class), st1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ goodfieldsandtypes(r, sks, st) ↔ (∀ sk. sk ∈ sks → goodfieldandtype(r, sk, st))
Proof step 18:
st[r -- _type] = typeval(mkclasstype(class)), st1[r -- _type] = typeval(mkclasstype(class)), r ∈ st1, r ∈ st, r -- _type ∈ st1, ∀ sk. sk ∈ instfields(class) → goodfieldandtype(r, sk, st), r -- _type ∈ st, ∀ rk. rk ∈ st → rk ∈ st1 ∧ st[rk] = st1[rk] ⊦ r = jvmref, ∀ sk. sk ∈ instfields(class) → goodfieldandtype(r, sk, st1)

Rule argument

[speclemmaarg: , goodfieldsandtypes(r, sks, st) ↔ (∀ sk. sk ∈ sks → goodfieldandtype(r, sk, st)) ,[st, sks, r] → [st1, instfields(class), r] ,F ,okfuns , ,gfts-all ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st1, instfields(class), r)]]