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Proof step 47 from proof initsubset-initerror-04 (previous step)

validstatfield(str, sk, st), sk ∈ statfields(class3), tdname∃(str, class3), initdone(class3, st0[jvmref -- mkfs(class, void_type, `initstate' .field) ', initval(error)]), initdone(class3, st), ∀ 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), 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 24:
⊦ sk ≠ sk0 ∧ ( ¬ is_fskey(sk) ∨ sk .fs .type ≠ void_type ∨ sk .fs ≠ mkfs(`java.lang.Object' .class, void_type, `uninit' .field) ∧ (¬ is_fskey(sk0) ∨ sk .fs ≠ mkfs(sk0 .fs .class, void_type, `initstate' .field))) → (validstatfield(str, sk0, st[jvmref -- sk, val]) ↔ validstatfield(str, sk0, st))
Proof step 35:
¬ ( mkfs(class, void_type, `initstate' .field) ' ≠ sk ∧ ( ¬ is_fskey(mkfs(class, void_type, `initstate' .field) ') ∨ mkfs(class, void_type, `initstate' .field) ' .fs .type ≠ void_type ∨ mkfs(class, void_type, `initstate' .field) ' .fs ≠ mkfs(`java.lang.Object' .class, void_type, `uninit' .field) ∧ (¬ is_fskey(sk) ∨ mkfs(class, void_type, `initstate' .field) ' .fs ≠ mkfs(sk .fs .class, void_type, `initstate' .field)))), validstatfield(str, sk, st), sk ∈ statfields(class3), tdname∃(str, class3), initdone(class3, st0[jvmref -- mkfs(class, void_type, `initstate' .field) ', initval(error)]), initdone(class3, st), ∀ 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), validstatfield(str, sk, st0[jvmref -- mkfs(class, void_type, `initstate' .field) ', initval(error)])
Proof step 46:
mkfs(class, void_type, `initstate' .field) ' ≠ sk ∧ ( ¬ is_fskey(mkfs(class, void_type, `initstate' .field) ') ∨ mkfs(class, void_type, `initstate' .field) ' .fs .type ≠ void_type ∨ mkfs(class, void_type, `initstate' .field) ' .fs ≠ mkfs(`java.lang.Object' .class, void_type, `uninit' .field) ∧ (¬ is_fskey(sk) ∨ mkfs(class, void_type, `initstate' .field) ' .fs ≠ mkfs(sk .fs .class, void_type, `initstate' .field))), validstatfield(str, sk, st), sk ∈ statfields(class3), tdname∃(str, class3), initdone(class3, st0[jvmref -- mkfs(class, void_type, `initstate' .field) ', initval(error)]), initdone(class3, st), ∀ 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), validstatfield(str, sk, st0)

Rule argument

[crewrite-arg: validstatfield-put-statfield , F , [val, sk, st, sk0, str] → [initval(error), mkfs(class, void_type, `initstate' .field) ', st0, sk, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (initval(error), mkfs(class, void_type, `initstate' .field) ', st0, sk, str)]]