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Proof step 9 from proof validstatfields-put-statfield-01 (previous step)

∀ sk, class, ty, fieldvar, str, st, val. sk .fs = mkfs(class, ty, fieldvar) ∧ (is_indexkey(sk) ∨ ty ≠ void_type ∨ fieldvar ≠ `initstate' .field ∧ sk .fs ≠ mkfs(`java.lang.Object' .class, void_type, `uninit' .field)) → (validstatfields(str, sks0, st[jvmref -- sk, val]) ↔ validstatfields(str, sks0, st)) ∨ sk ∈ sks0, sk .fs = mkfs(class, ty, fieldvar), is_indexkey(sk) ∨ ty ≠ void_type ∨ fieldvar ≠ `initstate' .field ∧ sk .fs ≠ mkfs(`java.lang.Object' .class, void_type, `uninit' .field) ⊦ validstatfields(str, sk0 + sks0, st[jvmref -- sk, val]) ↔ validstatfields(str, sk0 + sks0, st), sk ∈ sk0 + sks0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
⊦ validstatfields(str, sk ' + sks, st) ↔ validstatfield(str, sk, st) ∧ validstatfields(str, sks, st)
Proof step 8:
sk .fs = mkfs(class, ty, fieldvar), ∀ sk1, class0, ty0, fieldvar0, str0, st0, val0. sk1 .fs = mkfs(class0, ty0, fieldvar0) ∧ (¬ is_fskey(sk1) ∨ ty0 ≠ void_type ∨ fieldvar0 ≠ `initstate' .field ∧ sk1 .fs ≠ mkfs(`java.lang.Object' .class, void_type, `uninit' .field)) → (validstatfields(str0, sks0, st0[jvmref -- sk1, val0]) ↔ validstatfields(str0, sks0, st0)) ∨ sk1 ∈ sks0, is_indexkey(sk) ∨ ty ≠ void_type ∨ fieldvar ≠ `initstate' .field ∧ (class ≠ `java.lang.Object' .class ∨ fieldvar ≠ `uninit' .field) ⊦ sk = sk0, validstatfield(str, sk0, st[jvmref -- sk, val]) ∧ validstatfields(str, sks0, st[jvmref -- sk, val]) ↔ validstatfields(str, sk0 ' + sks0, st), sk ∈ sks0

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ mkfs(class1, ty, fieldvar) = mkfs(class2, ty0, fieldvar0) ↔ ¬ ¬ ( class1 = class2 ∧ ty = ty0 ∧ fieldvar = fieldvar0)], [CSIMPSEQ : ⊦ ¬ is_indexkey(sk) ↔ is_fskey(sk)], [CSIMPSEQ : ⊦ ¬ sk ∈ sk0 ' + sks ↔ sk ≠ sk0 ∧ ¬ sk ∈ sks], [CSIMPSEQ : ⊦ (sks + sks0) + sks1 = sks + sks0 + sks1], [CSIMPSEQ : ⊦ sk + sks = sk ' + sks])]]