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Proof step 9 from proof maxpath-object (previous step)

st[r -- _type] = typeval(mkclasstype(class0)), maxpath(str, r, st) = 1, st[r -- mkfs(class, ty, fieldvar) '] = refval(r0), r ∈ st, is_obj(str, r, st), mkfs(class, ty, fieldvar) ' ∈ instfields(class0), validrefs(str, r ', mkclasstype(class0), st), 1 ≤ maxpath(str, r0, st), goodfieldsandtypes(r, instfields(class0), st), r -- _type ∈ st ⊦ maxpath(str, r0, st) = 0, # validrefset(str, r, st) = 0, validrefset(str, r, st) = ∅, r = jvmref, is_reftype(ty), cyclic(str, r, st), junkref(str, r, st)

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 8:
st[r -- _type] = typeval(mkclasstype(class0)), maxpath(str, r, st) = 1, st[r -- mkfs(class, ty, fieldvar) '] = refval(r0), r ∈ st, is_obj(str, r, st), mkfs(class, ty, fieldvar) ' ∈ instfields(class0), validrefs(str, r ', mkclasstype(class0), st), 1 ≤ maxpath(str, r0, st), ∀ sk. sk ∈ instfields(class0) → goodfieldandtype(r, sk, st), r -- _type ∈ st ⊦ maxpath(str, r0, st) = 0, # validrefset(str, r, st) = 0, validrefset(str, r, st) = ∅, r = jvmref, is_reftype(ty), cyclic(str, r, st), junkref(str, r, st)

Rule argument

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

Additional information

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