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Proof step 14 from proof validstatfield-put-statfield (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ validfield(str, r, sk, st) ↔ goodfieldandtype(r, sk, st) ∧ type∃(str, sk .fs .type) ∧ sk .fs .type ≠ void_type ∧ (is_reftype(sk .fs .type) → validrefval(str, st[r -- sk], sk .fs .type, st))
Proof step 13:
sk .fs = mkfs(class0, ty0, fieldvar0), initdone(class, st), mkfs(class, ty, fieldvar) ' ∈ statfields(class), tdname∃(str, class), is_indexkey(sk) ∨ ty0 ≠ void_type ∨ (class0 ≠ `java.lang.Object' .class ∨ fieldvar0 ≠ `uninit' .field) ∧ (class0 ≠ class ∨ fieldvar0 ≠ `initstate' .field) ⊦ sk = mkfs(`java.lang.Object' .class, void_type, `uninit' .field) ', sk = mkfs(class, void_type, `initstate' .field) ', sk = mkfs(class, ty, fieldvar) ', validfield(str, jvmref, mkfs(class, ty, fieldvar) ', st[jvmref -- sk, val]) ↔ goodfieldandtype(jvmref, mkfs(class, ty, fieldvar) ', st) ∧ type∃(str, mkfs(class, ty, fieldvar) ' .fs .type) ∧ mkfs(class, ty, fieldvar) ' .fs .type ≠ void_type ∧ ( is_reftype(mkfs(class, ty, fieldvar) ' .fs .type) → validrefval(str, st[jvmref -- mkfs(class, ty, fieldvar) '], mkfs(class, ty, fieldvar) ' .fs .type, st))

Rule argument

[crewrite-arg: validfield-def , F , [st, sk, r, str] → [st, mkfs(class, ty, fieldvar) ', jvmref, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, mkfs(class, ty, fieldvar) ', jvmref, str)]]