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Proof step 45 from proof initsubset-put-statfield-01 (previous step)

init⊆(str, st, st0), ¬ mkfs(class, ty, fieldvar) ' ∈ statfields(class) ∨ ¬ tdname∃(str, class), ty ≠ void_type ∨ fieldvar ≠ `initstate' .field ∧ (class ≠ `java.lang.Object' .class ∨ fieldvar ≠ `uninit' .field) ⊦ (initdone(class0, st) → initdone(class0, st0[jvmref -- mkfs(class, ty, fieldvar) ', val])) ∧ (initerror(class1, st) → initerror(class1, st0[jvmref -- mkfs(class, ty, fieldvar) ', val])) ∧ ( ¬ initdone(class2, st) ∧ initdone(class2, st0[jvmref -- mkfs(class, ty, fieldvar) ', val]) ∧ tdname∃(str, class2) → validstatfields(str, statfields(class2), st0[jvmref -- mkfs(class, ty, fieldvar) ', val])) ∧ ( initdone(class3, st) ∧ initdone(class3, st0[jvmref -- mkfs(class, ty, fieldvar) ', val]) ∧ tdname∃(str, class3) ∧ sk ∈ statfields(class3) ∧ validstatfield(str, sk, st) → validstatfield(str, sk, st0[jvmref -- mkfs(class, ty, fieldvar) ', val]))

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 44:
(∀ 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)), ¬ mkfs(class, ty, fieldvar) ' ∈ statfields(class) ∨ ¬ tdname∃(str, class), ty ≠ void_type ∨ fieldvar ≠ `initstate' .field ∧ (class ≠ `java.lang.Object' .class ∨ fieldvar ≠ `uninit' .field) ⊦ (initdone(class0, st) → initdone(class0, st0[jvmref -- mkfs(class, ty, fieldvar) ', val])) ∧ (initerror(class1, st) → initerror(class1, st0[jvmref -- mkfs(class, ty, fieldvar) ', val])) ∧ ( ¬ initdone(class2, st) ∧ initdone(class2, st0[jvmref -- mkfs(class, ty, fieldvar) ', val]) ∧ tdname∃(str, class2) → validstatfields(str, statfields(class2), st0[jvmref -- mkfs(class, ty, fieldvar) ', val])) ∧ ( initdone(class3, st) ∧ initdone(class3, st0[jvmref -- mkfs(class, ty, fieldvar) ', val]) ∧ tdname∃(str, class3) ∧ sk ∈ statfields(class3) ∧ validstatfield(str, sk, st) → validstatfield(str, sk, st0[jvmref -- mkfs(class, ty, fieldvar) ', val]))

Rule argument

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

Additional information

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