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Proof step 15 from proof isobj-subset (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ is_fskey(sk) → (goodfieldandtype(r, sk, st) ↔ r -- sk ∈ st ∧ okval(st[r -- sk], sk .fs .type))
Proof step 14:
is_fskey(sk), st1[r -- _type] = typeval(mkclasstype(class)), st[r -- _type] = typeval(mkclasstype(class)), r -- _type ∈ st, r -- _type ∈ st1, r ∈ st, r ∈ st1, sk ∈ instfields(class), goodfieldandtype(r, sk, st), ∀ sk. sk ∈ instfields(class) → goodfieldandtype(r, sk, st), ∀ rk. rk ∈ st → rk ∈ st1 ∧ st[rk] = st1[rk] ⊦ r = jvmref, r -- sk ∈ st1 ∧ okval(st1[r -- sk], sk .fs .type)

Rule argument

[speclemmaarg: , is_fskey(sk) → ( goodfieldandtype(r, sk, st) ↔ r -- sk ∈ st ∧ okval(st[r -- sk], sk .fs .type)) ,[st, sk, r] → [st1, sk, r] ,F ,okfuns , ,good-field-field ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ is_fskey(sk) ↔ is_indexkey(sk)], [CSIMPSEQ : ⊦ is_indexkey(sk) → ¬ goodfieldandtype(r, sk, st)])], [EXTRATERMS : (st1, sk, r)]]