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Proof step 38 from proof initsubset-trans (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ init⊆(str, st, st0) ↔ (∀ 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))
Proof step 37:
∀ class. initdone(class, st0) → initdone(class, st1), ∀ class. initerror(class, st0) → initerror(class, st1), ∀ class. ¬ initdone(class, st0) ∧ initdone(class, st1) ∧ tdname∃(str, class) → validstatfields(str, statfields(class), st1), ∀ class, sk. initdone(class, st0) ∧ initdone(class, st1) ∧ tdname∃(str, class) ∧ sk ∈ statfields(class) ∧ validstatfield(str, sk, st0) → validstatfield(str, sk, st1), ∀ 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) ⊦ (∀ class. initdone(class, st) → initdone(class, st1)) ∧ (∀ class. initerror(class, st) → initerror(class, st1)) ∧ (∀ class. ¬ initdone(class, st) ∧ initdone(class, st1) ∧ tdname∃(str, class) → validstatfields(str, statfields(class), st1)) ∧ (∀ class, sk. initdone(class, st) ∧ initdone(class, st1) ∧ tdname∃(str, class) ∧ sk ∈ statfields(class) ∧ validstatfield(str, sk, st) → validstatfield(str, sk, st1))

Rule argument

[crewrite-arg: initsubset-def, F, [st0, st, str] → [st1, st, str]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st1, st, str)]]