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Proof step 51 from proof initsubset-initerror-04 (previous step)

init⊆(str, st, st0) ⊦ initdone(class, st), (initdone(class0, st) → initdone(class0, st0[jvmref -- mkfs(class, void_type, `initstate' .field) ', initval(error)])) ∧ (initerror(class1, st) → initerror(class1, st0[jvmref -- mkfs(class, void_type, `initstate' .field) ', initval(error)])) ∧ ( ¬ initdone(class2, st) ∧ initdone(class2, st0[jvmref -- mkfs(class, void_type, `initstate' .field) ', initval(error)]) ∧ tdname∃(str, class2) → validstatfields(str, statfields(class2), st0[jvmref -- mkfs(class, void_type, `initstate' .field) ', initval(error)])) ∧ ( initdone(class3, st) ∧ initdone(class3, st0[jvmref -- mkfs(class, void_type, `initstate' .field) ', initval(error)]) ∧ tdname∃(str, class3) ∧ sk ∈ statfields(class3) ∧ validstatfield(str, sk, st) → validstatfield(str, sk, st0[jvmref -- mkfs(class, void_type, `initstate' .field) ', initval(error)]))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ 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 50:
(∀ 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)) ⊦ initdone(class, st), (initdone(class0, st) → initdone(class0, st0[jvmref -- mkfs(class, void_type, `initstate' .field) ', initval(error)])) ∧ (initerror(class1, st) → initerror(class1, st0[jvmref -- mkfs(class, void_type, `initstate' .field) ', initval(error)])) ∧ ( ¬ initdone(class2, st) ∧ initdone(class2, st0[jvmref -- mkfs(class, void_type, `initstate' .field) ', initval(error)]) ∧ tdname∃(str, class2) → validstatfields(str, statfields(class2), st0[jvmref -- mkfs(class, void_type, `initstate' .field) ', initval(error)])) ∧ ( initdone(class3, st) ∧ initdone(class3, st0[jvmref -- mkfs(class, void_type, `initstate' .field) ', initval(error)]) ∧ tdname∃(str, class3) ∧ sk ∈ statfields(class3) ∧ validstatfield(str, sk, st) → validstatfield(str, sk, st0[jvmref -- mkfs(class, void_type, `initstate' .field) ', initval(error)]))

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st0, st, str)]]