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Proof step 30 from proof initsubset-initerror-04 (previous step)

initdone(class3, st), initdone(class3, st0[jvmref -- mkfs(class0, void_type, `initstate' .field) ', initval(error)]), tdname∃(str, class3), mkfs(class0, ty, fieldvar) ' ∈ statfields(class3), validstatfield(str, mkfs(class0, ty, fieldvar) ', st), ∀ 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) ⊦ void_type = ty, validstatfield(str, mkfs(class0, ty, fieldvar) ', st0[jvmref -- mkfs(class0, void_type, `initstate' .field) ', initval(error)]), initdone(class0, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 26:
⊦ rk ≠ jvmref -- mkfs(class, void_type, `initstate' .field) ' ∧ rk ≠ _uninit → (initdone(class, st[rk, val]) ↔ initdone(class, st))
Proof step 29:
jvmref -- mkfs(class0, void_type, `initstate' .field) ' ≠ jvmref -- mkfs(class3, void_type, `initstate' .field) ' ∧ jvmref -- mkfs(class0, void_type, `initstate' .field) ' ≠ _uninit, initdone(class3, st), initdone(class3, st0), tdname∃(str, class3), mkfs(class0, ty, fieldvar) ' ∈ statfields(class3), validstatfield(str, mkfs(class0, ty, fieldvar) ', st), ∀ 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) ⊦ void_type = ty, validstatfield(str, mkfs(class0, ty, fieldvar) ', st0[jvmref -- mkfs(class0, void_type, `initstate' .field) ', initval(error)]), initdone(class0, st)

Rule argument

[speclemmaarg: , rk ≠ jvmref -- mkfs(class, void_type, `initstate' .field) ' ∧ rk ≠ _uninit → (initdone(class, st[rk, val]) ↔ initdone(class, st)) ,[val, rk, st, class] → [initval(error), jvmref -- mkfs(class0, void_type, `initstate' .field) ', st0, class3] ,F ,storefuns , ,init-put-04 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0], [CSIMPSEQ : ⊦ fs ' = fs0 ' ↔ fs = fs0], [CSIMPSEQ : ⊦ mkfs(class, ty, fieldvar) = mkfs(class0, ty0, fieldvar0) ↔ class = class0 ∧ ty = ty0 ∧ fieldvar = fieldvar0], [CSIMPSEQ : ⊦ jvmref -- sk = _uninit ↔ sk = mkfs (`java.lang.Object' .class, void_type, `uninit' .field) '], [CSIMPSEQ : ⊦ stringvar .field = stringvar0 .field ↔ stringvar = stringvar0])], [EXTRATERMS : (initval(error), jvmref -- mkfs(class0, void_type, `initstate' .field) ', st0, class3)]]