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Proof step 24 from proof initsubset-put-statfield-01 (previous step)

sk .fs = mkfs(class4, ty0, fieldvar0), validstatfield(str, sk, st), sk ∈ statfields(class3), tdname∃(str, class3), initdone(class3, st0), initdone(class3, st), class ≠ class3 ∨ ty ≠ void_type ∨ fieldvar ≠ `initstate' .field, class ≠ class2 ∨ ty ≠ void_type ∨ fieldvar ≠ `initstate' .field, class ≠ class1 ∨ ty ≠ void_type ∨ fieldvar ≠ `initstate' .field, class ≠ class0 ∨ ty ≠ void_type ∨ fieldvar ≠ `initstate' .field, class ≠ `java.lang.Object' .class ∨ ty ≠ void_type ∨ fieldvar ≠ `uninit' .field, initdone(class0, st) → initdone(class0, st0), initerror(class1, st) → initerror(class1, 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) ⊦ validstatfield(str, sk, st0[jvmref -- mkfs(class, ty, fieldvar) ', val]), mkfs(class, ty, fieldvar) ' ≠ sk ∧ ( ty ≠ void_type ∨ (class ≠ `java.lang.Object' .class ∨ fieldvar ≠ `uninit' .field) ∧ (¬ is_fskey(sk) ∨ class ≠ class4 ∨ fieldvar ≠ `initstate' .field))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ validstatfield(str, sk, st) ↔ is_fskey(sk) ∧ sk ∈ statfields(sk .fs .class) ∧ tdname∃(str, sk .fs .class) ∧ (initdone(sk .fs .class, st) → validfield(str, jvmref, sk, st))
Proof step 23:
sk .fs = mkfs(class4, ty0, fieldvar0), validstatfield(str, sk, st), sk ∈ statfields(class3), tdname∃(str, class3), initdone(class3, st0), initdone(class3, st), class ≠ class3 ∨ ty ≠ void_type ∨ fieldvar ≠ `initstate' .field, class ≠ class2 ∨ ty ≠ void_type ∨ fieldvar ≠ `initstate' .field, class ≠ class1 ∨ ty ≠ void_type ∨ fieldvar ≠ `initstate' .field, class ≠ class0 ∨ ty ≠ void_type ∨ fieldvar ≠ `initstate' .field, class ≠ `java.lang.Object' .class ∨ ty ≠ void_type ∨ fieldvar ≠ `uninit' .field, initdone(class0, st) → initdone(class0, st0), initerror(class1, st) → initerror(class1, 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) ⊦ is_fskey(sk) ∧ sk ∈ statfields(sk .fs .class) ∧ tdname∃(str, sk .fs .class) ∧ ( initdone(sk .fs .class, st0[jvmref -- mkfs(class, ty, fieldvar) ', val]) → validfield(str, jvmref, sk, st0[jvmref -- mkfs(class, ty, fieldvar) ', val])), mkfs(class, ty, fieldvar) ' ≠ sk ∧ ( ty ≠ void_type ∨ (class ≠ `java.lang.Object' .class ∨ fieldvar ≠ `uninit' .field) ∧ (¬ is_fskey(sk) ∨ class ≠ class4 ∨ fieldvar ≠ `initstate' .field))

Rule argument

[crewrite-arg: validstatfield-storekey-def , F , [st, sk, str] → [st0[jvmref -- mkfs(class, ty, fieldvar) ', val], sk, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st0[jvmref -- mkfs(class, ty, fieldvar) ', val], sk, str)]]