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Proof step 17 from proof compatobj-isobj (previous step)

st[r -- _type] = typeval(mkclasstype(class)), r ∈ st, r -- _type ∈ st, class+∃(str, class), sk ∈ instfields(class), ∀ sk. sk ∈ instfields(class) → r -- sk ∈ st ∧ is_fskey(sk) ∧ compat(str, st[r -- sk], sk .fs .type, st) ⊦ r = jvmref, goodfieldandtype(r, sk, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ is_fskey(sk) → (goodfieldandtype(r, sk, st) ↔ r -- sk ∈ st ∧ oktype(st[r -- sk], sk .fs .type, st))
Proof step 8:
¬ is_fskey(sk), st[r -- _type] = typeval(mkclasstype(class)), r ∈ st, r -- _type ∈ st, class+∃(str, class), sk ∈ instfields(class), ∀ sk. sk ∈ instfields(class) → r -- sk ∈ st ∧ is_fskey(sk) ∧ compat(str, st[r -- sk], sk .fs .type, st) ⊦ r = jvmref, goodfieldandtype(r, sk, st)
Proof step 16:
is_fskey(sk), st[r -- _type] = typeval(mkclasstype(class)), r ∈ st, r -- _type ∈ st, class+∃(str, class), sk ∈ instfields(class), ∀ sk. sk ∈ instfields(class) → r -- sk ∈ st ∧ is_fskey(sk) ∧ compat(str, st[r -- sk], sk .fs .type, st) ⊦ r = jvmref, r -- sk ∈ st ∧ oktype(st[r -- sk], sk .fs .type, st)

Rule argument

[speclemmaarg: , is_fskey(sk) → ( goodfieldandtype(r, sk, st) ↔ r -- sk ∈ st ∧ oktype(st[r -- sk], sk .fs .type, st)) ,[st, sk, r] → [st, sk, r] ,F ,okfuns , ,good-field-02 ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, sk, r)]]