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Proof step 29 from proof initsubset-trans (previous step)

tdname∃(str, class), initdone(class, st1), ∀ class. initdone(class, st) → initdone(class, st0), ∀ class. initerror(class, st) → initerror(class, st0), ∀ class. ¬ initdone(class, st) ∧ initdone(class, st0) ∧ tdname∃(str, class) → validstatfields(str, statfields(class), st0), ∀ class, sk. initdone(class, st) ∧ initdone(class, st0) ∧ tdname∃(str, class) ∧ sk ∈ statfields(class) ∧ validstatfield(str, sk, st) → validstatfield(str, sk, st0), ∀ class, sk. initdone(class, st0) ∧ initdone(class, st1) ∧ tdname∃(str, class) ∧ sk ∈ statfields(class) ∧ validstatfield(str, sk, st0) → validstatfield(str, sk, st1), ∀ class. ¬ initdone(class, st0) ∧ initdone(class, st1) ∧ tdname∃(str, class) → validstatfields(str, statfields(class), st1), ∀ class. initerror(class, st0) → initerror(class, st1), ∀ class. initdone(class, st0) → initdone(class, st1) ⊦ initdone(class, st), validstatfields(str, statfields(class), st1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ validstatfields(str, sks, st) ↔ (∀ sk. sk ∈ sks → validstatfield(str, sk, st))
Proof step 28:
tdname∃(str, class), initdone(class, st1), ∀ class. initdone(class, st) → initdone(class, st0), ∀ class. initerror(class, st) → initerror(class, st0), ∀ class. ¬ initdone(class, st) ∧ initdone(class, st0) ∧ tdname∃(str, class) → validstatfields(str, statfields(class), st0), ∀ class, sk. initdone(class, st) ∧ initdone(class, st0) ∧ tdname∃(str, class) ∧ sk ∈ statfields(class) ∧ validstatfield(str, sk, st) → validstatfield(str, sk, st0), ∀ class, sk. initdone(class, st0) ∧ initdone(class, st1) ∧ tdname∃(str, class) ∧ sk ∈ statfields(class) ∧ validstatfield(str, sk, st0) → validstatfield(str, sk, st1), ∀ class. ¬ initdone(class, st0) ∧ initdone(class, st1) ∧ tdname∃(str, class) → validstatfields(str, statfields(class), st1), ∀ class. initerror(class, st0) → initerror(class, st1), ∀ class. initdone(class, st0) → initdone(class, st1) ⊦ initdone(class, st), ∀ sk. sk ∈ statfields(class) → validstatfield(str, sk, st1)

Rule argument

[crewrite-arg: validstatfields-storekeys-def , F , [st, sks, str] → [st1, statfields(class), str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st1, statfields(class), str)]]