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Proof step 10 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), jvmref -- mkfs(class, ty, fieldvar) ' ∈ st, okval(st[jvmref -- mkfs(class, ty, fieldvar) '], ty), type∃(str, ty), jvmref ∈ st, is_indexkey(sk) ∨ ty0 ≠ void_type ∨ (class0 ≠ `java.lang.Object' .class ∨ fieldvar0 ≠ `uninit' .field) ∧ (class0 ≠ class ∨ fieldvar0 ≠ `initstate' .field), is_reftype(ty) → validrefval(str, st[jvmref -- mkfs(class, ty, fieldvar) '], ty, st) ⊦ sk = mkfs(`java.lang.Object' .class, void_type, `uninit' .field) ', sk = mkfs(class, void_type, `initstate' .field) ', sk = mkfs(class, ty, fieldvar) ', ty = void_type, goodfieldandtype(jvmref, mkfs(class, ty, fieldvar) ', st[jvmref -- sk, val])

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[speclemmaarg: , goodfieldandtype(r, sk, st) ↔ is_fskey(sk) ∧ r -- sk ∈ st ∧ okval(st[r -- sk], sk .fs .type) ,[st, sk, r] → [st[jvmref -- sk, val], mkfs(class, ty, fieldvar) ', jvmref] ,F ,okfuns , ,good-field-def ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_fskey(fs ')], [CSIMPSEQ : sk ≠ sk0 ⊦ r -- sk ∈ st[r -- sk0, val] ↔ r -- sk ∈ st], [CSIMPSEQ : ⊦ sk ≠ sk0 → (st[r -- sk, val][r0 -- sk0]) = st[r0 -- sk0]], [CSIMPSEQ : ⊦ fs ' .fs = fs], [CSIMPSEQ : ⊦ mkfs(class, ty, fieldvar) .type = ty])], [EXTRATERMS : (st[jvmref -- sk, val], mkfs(class, ty, fieldvar) ', jvmref)]]