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Proof step 22 from proof initsubset-put-statfield-01 (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 21:
sk = fs ', fs = mkfs(class4, ty0, fieldvar0), is_fskey(sk), initdone(class3, st), initdone(class3, st0), tdname∃(str, class3), sk ∈ statfields(class3), validstatfield(str, sk, st), ty ≠ void_type ∨ fieldvar ≠ `initstate' .field ∧ (class ≠ `java.lang.Object' .class ∨ fieldvar ≠ `uninit' .field), ¬ mkfs(class, ty, fieldvar) ' ∈ statfields(class) ∨ ¬ tdname∃(str, class), ∀ 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), initerror(class1, st) → initerror(class1, st0), initdone(class0, st) → initdone(class0, st0), class ≠ `java.lang.Object' .class ∨ ty ≠ void_type ∨ fieldvar ≠ `uninit' .field, class ≠ class0 ∨ ty ≠ void_type ∨ fieldvar ≠ `initstate' .field, class ≠ class1 ∨ ty ≠ void_type ∨ fieldvar ≠ `initstate' .field, class ≠ class2 ∨ ty ≠ void_type ∨ fieldvar ≠ `initstate' .field, class ≠ class3 ∨ ty ≠ void_type ∨ fieldvar ≠ `initstate' .field ⊦ mkfs(class, ty, fieldvar) ' ≠ sk ∧ (ty ≠ void_type ∨ (class ≠ `java.lang.Object' .class ∨ fieldvar ≠ `uninit' .field) ∧ (class ≠ class4 ∨ fieldvar ≠ `initstate' .field)), (initdone(class4, st0[jvmref -- mkfs(class, ty, fieldvar) ', val]) → validfield(str, jvmref, sk, st0[jvmref -- mkfs(class, ty, fieldvar) ', val])) ∧ tdname∃(str, class4) ∧ sk ∈ statfields(class4)

Rule argument

[speclemmaarg: ,is_fskey(sk) → (fs = sk .fs ↔ sk = fs ') ,[sk, fs] → [sk, fs] ,T ,storekey , ,elim-03 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_fskey(sk) → (fs = sk .fs ↔ sk = fs ')])], [EXTRATERMS : (sk, fs)]]