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Proof step 14 from proof initsubset-addclass (previous step)

fis .keys = statfields(class), initundone(class, st), validfieldinits(str, fis, st) ⊦ class = `java.lang.Object' .class, init⊆(str, st, addclass(class, fis, st))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ 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 13:
fis .keys = statfields(class), initundone(class, st), validfieldinits(str, fis, st) ⊦ class = `java.lang.Object' .class, (∀ class0. initdone(class0, st) → initdone(class0, addclass(class, fis, st))) ∧ (∀ class0. initerror(class0, st) → initerror(class0, addclass(class, fis, st))) ∧ (∀ class0. ¬ initdone(class0, st) ∧ initdone(class0, addclass(class, fis, st)) ∧ tdname∃(str, class0) → validstatfields(str, statfields(class0), addclass(class, fis, st))) ∧ (∀ class0, sk. initdone(class0, st) ∧ initdone(class0, addclass(class, fis, st)) ∧ tdname∃(str, class0) ∧ sk ∈ statfields(class0) ∧ validstatfield(str, sk, st) → validstatfield(str, sk, addclass(class, fis, st)))

Rule argument

[crewrite-arg: initsubset-def , F , [st0, st, str] → [addclass(class, fis, st), st, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (addclass(class, fis, st), st, str)]]