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Proof step 7 from proof validstatfields-put-statfield-02 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ validstatfields(str, sks, st) ↔ (∀ sk. sk ∈ sks → validstatfield(str, sk, st))
Proof step 6:
sk .fs = mkfs(class, ty, fieldvar), sk0 ∈ sks, validstatfield(str, sk, st[jvmref -- sk, val]), ∀ sk. sk ∈ sks → validstatfield(str, sk, st), is_fskey(sk), fieldvar ≠ `initstate' .field ∧ (class ≠ `java.lang.Object' .class ∨ fieldvar ≠ `uninit' .field) ∨ ty ≠ void_type, (class ≠ `java.lang.Object' .class ∨ fieldvar ≠ `uninit' .field) ∧ (is_indexkey(sk0) ∨ class ≠ sk0 .fs .class ∨ fieldvar ≠ `initstate' .field) ∨ ty ≠ void_type ⊦ sk = sk0, validstatfield(str, sk0, st)

Rule argument

[crewrite-arg: validstatfields-storekeys-def , F , [st, sks, str] → [st, sks, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, sks, str)]]