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Proof step 29 from proof initsubset-validstatfield-forward (previous step)

validstatfield(str, sk, st), ∀ class, sk. initdone(class, st) ∧ initdone(class, st0) ∧ tdname∃(str, class) ∧ sk ∈ statfields(class) ∧ validstatfield(str, sk, st) → validstatfield(str, sk, st0), ∀ class. ¬ initdone(class, st) ∧ initdone(class, st0) ∧ tdname∃(str, class) → validstatfields(str, statfields(class), st0), ∀ class. initerror(class, st) → initerror(class, st0), ∀ class. initdone(class, st) → initdone(class, st0) ⊦ validstatfield(str, sk, st0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ validstatfield(str, sk, st) ↔ is_fskey(sk) ∧ sk ∈ statfields(sk .fs .class) ∧ tdname∃(str, sk .fs .class) ∧ (initdone(sk .fs .class, st) → validfield(str, jvmref, sk, st))
Proof step 28:
is_fskey(sk) ∧ sk ∈ statfields(sk .fs .class) ∧ tdname∃(str, sk .fs .class) ∧ (initdone(sk .fs .class, st) → validfield(str, jvmref, sk, st)), ∀ class, sk. initdone(class, st) ∧ initdone(class, st0) ∧ tdname∃(str, class) ∧ sk ∈ statfields(class) ∧ validstatfield(str, sk, st) → validstatfield(str, sk, st0), ∀ class. ¬ initdone(class, st) ∧ initdone(class, st0) ∧ tdname∃(str, class) → validstatfields(str, statfields(class), st0), ∀ class. initerror(class, st) → initerror(class, st0), ∀ class. initdone(class, st) → initdone(class, st0) ⊦ validstatfield(str, sk, st0)

Rule argument

[crewrite-arg: validstatfield-storekey-def , F , [st, sk, str] → [st, sk, str] ]

Additional information

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