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Proof step 12 from proof validrefs-lastelem (previous step)

st[r0 -- _type] = typeval(mkclasstype(class0)), st[r0 -- mkfs(class, ty0, fieldvar) '] = refval(r1), mkfs(class, ty0, fieldvar) ' ∈ instfields(class0), goodfieldsandtypes(r0, instfields(class0), st), r0 -- _type ∈ st, r0 ∈ st, validrefs(str, r1 ', ty0, st), is_obj(str, r0, st), class0 ≤ class1 ⊦ r0 = jvmref, is_reftype(ty0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ goodfieldsandtypes(r, sks, st) ↔ (∀ sk. sk ∈ sks → goodfieldandtype(r, sk, st))
Proof step 11:
st[r0 -- _type] = typeval(mkclasstype(class0)), st[r0 -- mkfs(class, ty0, fieldvar) '] = refval(r1), mkfs(class, ty0, fieldvar) ' ∈ instfields(class0), ∀ sk. sk ∈ instfields(class0) → goodfieldandtype(r0, sk, st), r0 -- _type ∈ st, r0 ∈ st, validrefs(str, r1 ', ty0, st), is_obj(str, r0, st), class0 ≤ class1 ⊦ r0 = jvmref, is_reftype(ty0)

Rule argument

[speclemmaarg: , goodfieldsandtypes(r, sks, st) ↔ (∀ sk. sk ∈ sks → goodfieldandtype(r, sk, st)) ,[st, sks, r] → [st, instfields(class0), r0] ,F ,okfuns , ,gfts-all ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, instfields(class0), r0)]]