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Proof step 11 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) ', goodfieldandtype(jvmref, mkfs(class, ty, fieldvar) ', st[jvmref -- sk, val]) ∧ 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 -- sk, val][jvmref -- mkfs(class, ty, fieldvar) '], mkfs(class, ty, fieldvar) ' .fs .type, st[jvmref -- sk, val])) ↔ goodfieldandtype(jvmref, mkfs(class, ty, fieldvar) ', st) ∧ type∃(str, ty) ∧ ty ≠ void_type ∧ (is_reftype(ty) → validrefval(str, st[jvmref -- mkfs(class, ty, fieldvar) '], ty, st))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
⊦ validrefval(str, val, ty, st[jvmref -- sk, val0]) ↔ validrefval(str, val, ty, st)
Proof step 10:
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])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPSEQ : ⊦ mkfs(class, ty, fieldvar) .type = ty], [CSIMPSEQ : ⊦ fs ' .fs = fs], [CSIMPSEQ : ⊦ sk ≠ sk0 → (st[r -- sk, val][r0 -- sk0]) = st[r0 -- sk0]], [CSIMPSEQ : sk ≠ sk0 ⊦ r -- sk ∈ st[r -- sk0, val] ↔ r -- sk ∈ st], [CSIMPSEQ : ⊦ goodfieldandtype (r, mkfs(class1, ty, fieldvar) ', st) ↔ r -- mkfs(class1, ty, fieldvar) ' ∈ st ∧ okval (st[ r -- mkfs (class1, ty, fieldvar) '], ty)])]]