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Proof step 24 from proof validstatfield-put-statfield (previous step)

sk .fs = mkfs(class0, ty0, fieldvar0), sk0 .fs = mkfs(class, ty, fieldvar), is_indexkey(sk) ∨ ty0 ≠ void_type ∨ (class0 ≠ `java.lang.Object' .class ∨ fieldvar0 ≠ `uninit' .field) ∧ (is_indexkey(sk0) ∨ class0 ≠ class ∨ fieldvar0 ≠ `initstate' .field) ⊦ sk = sk0, validstatfield(str, sk0, st[jvmref -- sk, val]) ↔ ¬ is_indexkey(sk0) ∧ sk0 ∈ statfields(class) ∧ tdname∃(str, class) ∧ (initdone(class, st) → validfield(str, jvmref, sk0, st))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ 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(class0, ty0, fieldvar0), sk0 .fs = mkfs(class, ty, fieldvar), is_indexkey(sk) ∨ ty0 ≠ void_type ∨ (class0 ≠ `java.lang.Object' .class ∨ fieldvar0 ≠ `uninit' .field) ∧ (is_indexkey(sk0) ∨ class0 ≠ class ∨ fieldvar0 ≠ `initstate' .field) ⊦ sk = sk0, is_fskey(sk0) ∧ sk0 ∈ statfields(sk0 .fs .class) ∧ tdname∃(str, sk0 .fs .class) ∧ (initdone(sk0 .fs .class, st[jvmref -- sk, val]) → validfield(str, jvmref, sk0, st[jvmref -- sk, val])) ↔ ¬ is_indexkey(sk0) ∧ sk0 ∈ statfields(class) ∧ tdname∃(str, class) ∧ (initdone(class, st) → validfield(str, jvmref, sk0, st))

Rule argument

[crewrite-arg: validstatfield-storekey-def , F , [st, sk, str] → [st[jvmref -- sk, val], sk0, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st[jvmref -- sk, val], sk0, str)]]