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Proof step 19 from proof initsubset-put-statfield (previous step)

sk .fs = mkfs(class, ty, fieldvar), initdone(class3, st), initdone(class3, st0), tdname∃(str, class3), sk0 ∈ statfields(class3), validstatfield(str, sk0, st), validstatfield(str, sk, st0[jvmref -- sk, val]), is_fskey(sk), validstatfield(str, sk0, st0), ∀ class, sk. initdone(class, st) ∧ initdone(class, st0) ∧ tdname∃(str, class) ∧ sk ∈ statfields(class) ∧ validstatfield(str, sk, st) → validstatfield(str, sk, st0), fieldvar ≠ `initstate' .field ∨ ty ≠ void_type, initdone(class0, st) → initdone(class0, st0), initdone(class1, st) → initdone(class1, st0), ∀ class. initdone(class, st) → initdone(class, st0), initerror(class1, st) → initerror(class1, st0), ∀ class. initerror(class, st) → initerror(class, st0), ¬ initdone(class2, st) ∧ initdone(class2, st0) ∧ tdname∃(str, class2) → validstatfields(str, statfields(class2), st0), ∀ class. ¬ initdone(class, st) ∧ initdone(class, st0) ∧ tdname∃(str, class) → validstatfields(str, statfields(class), st0) ⊦ sk = mkfs(`java.lang.Object' .class, void_type, `uninit' .field) ', sk = mkfs(class0, void_type, `initstate' .field) ', sk = mkfs(class2, void_type, `initstate' .field) ', sk = mkfs(class3, void_type, `initstate' .field) ', validstatfield(str, sk0, st0[jvmref -- sk, val])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ 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 18:
¬ ( 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)))), sk .fs = mkfs(class, ty, fieldvar), initdone(class3, st), initdone(class3, st0), tdname∃(str, class3), sk0 ∈ statfields(class3), validstatfield(str, sk0, st), validstatfield(str, sk, st0[jvmref -- sk, val]), is_fskey(sk), validstatfield(str, sk0, st0), ∀ class, sk. initdone(class, st) ∧ initdone(class, st0) ∧ tdname∃(str, class) ∧ sk ∈ statfields(class) ∧ validstatfield(str, sk, st) → validstatfield(str, sk, st0), fieldvar ≠ `initstate' .field ∨ ty ≠ void_type, initdone(class0, st) → initdone(class0, st0), initdone(class1, st) → initdone(class1, st0), ∀ class. initdone(class, st) → initdone(class, st0), initerror(class1, st) → initerror(class1, st0), ∀ class. initerror(class, st) → initerror(class, st0), ¬ initdone(class2, st) ∧ initdone(class2, st0) ∧ tdname∃(str, class2) → validstatfields(str, statfields(class2), st0), ∀ class. ¬ initdone(class, st) ∧ initdone(class, st0) ∧ tdname∃(str, class) → validstatfields(str, statfields(class), st0) ⊦ sk = mkfs(`java.lang.Object' .class, void_type, `uninit' .field) ', sk = mkfs(class0, void_type, `initstate' .field) ', sk = mkfs(class2, void_type, `initstate' .field) ', sk = mkfs(class3, void_type, `initstate' .field) ', validstatfield(str, sk0, st0[jvmref -- sk, val])

Rule argument

[crewrite-arg: validstatfield-put-statfield , F , [val, sk, st, sk0, str] → [val, sk, st0, sk0, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (val, sk, st0, sk0, str)]]