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Proof step 27 from proof validstatfield-put-norefval (previous step)

okval(val, ty0), mkfs(class, ty, fieldvar) ' ∈ statfields(class), tdname∃(str, class), initdone(class, st), jvmref -- mkfs(class, ty, fieldvar) ' ∈ st, okval(st[jvmref -- mkfs(class, ty, fieldvar) '], ty), type∃(str, ty), jvmref ∈ st, jvmref ≠ r ∨ class ≠ class0 ∨ ty ≠ ty0 ∨ fieldvar ≠ fieldvar0, is_reftype(ty) → validrefval(str, st[jvmref -- mkfs(class, ty, fieldvar) '], ty, st) ⊦ mkfs(class0, ty0, fieldvar0) ' = _length, ty0 = void_type, r -- mkfs(class0, ty0, fieldvar0) ' = _uninit, ty = void_type, is_referencevalue(val), ( is_reftype(ty) → validrefval (str, st[r -- mkfs(class0, ty0, fieldvar0) ', val][jvmref -- mkfs(class, ty, fieldvar) '], ty, st[r -- mkfs(class0, ty0, fieldvar0) ', val])) ∧ goodfieldandtype(jvmref, mkfs(class, ty, fieldvar) ', st[r -- mkfs(class0, ty0, fieldvar0) ', val])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ goodfieldandtype(r, sk, st) ↔ is_fskey(sk) ∧ r -- sk ∈ st ∧ okval(st[r -- sk], sk .fs .type)
Proof step 26:
okval(val, ty0), mkfs(class, ty, fieldvar) ' ∈ statfields(class), tdname∃(str, class), initdone(class, st), jvmref -- mkfs(class, ty, fieldvar) ' ∈ st, okval(st[jvmref -- mkfs(class, ty, fieldvar) '], ty), type∃(str, ty), jvmref ∈ st, jvmref ≠ r ∨ class ≠ class0 ∨ ty ≠ ty0 ∨ fieldvar ≠ fieldvar0, is_reftype(ty) → validrefval(str, st[jvmref -- mkfs(class, ty, fieldvar) '], ty, st) ⊦ mkfs(class0, ty0, fieldvar0) ' = _length, ty0 = void_type, r -- mkfs(class0, ty0, fieldvar0) ' = _uninit, ty = void_type, is_referencevalue(val), ( is_reftype(ty) → validrefval (str, st[r -- mkfs(class0, ty0, fieldvar0) ', val][jvmref -- mkfs(class, ty, fieldvar) '], ty, st[r -- mkfs(class0, ty0, fieldvar0) ', val])) ∧ is_fskey(mkfs(class, ty, fieldvar) ') ∧ jvmref -- mkfs(class, ty, fieldvar) ' ∈ st[r -- mkfs(class0, ty0, fieldvar0) ', val] ∧ okval(st[r -- mkfs(class0, ty0, fieldvar0) ', val][jvmref -- mkfs(class, ty, fieldvar) '], mkfs(class, ty, fieldvar) ' .fs .type)

Rule argument

[speclemmaarg: , goodfieldandtype(r, sk, st) ↔ is_fskey(sk) ∧ r -- sk ∈ st ∧ okval(st[r -- sk], sk .fs .type) ,[st, sk, r] → [st[r -- mkfs(class0, ty0, fieldvar0) ', val], mkfs(class, ty, fieldvar) ', jvmref] ,F ,okfuns , ,good-field-def ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st[r -- mkfs(class0, ty0, fieldvar0) ', val], mkfs(class, ty, fieldvar) ', jvmref)]]