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Proof step 12 from proof validstatfield-union (previous step)

tdname∃(str, class), mkfs(class, ty, fieldvar) ' ∈ statfields(class), initdone(class, st0), validfield(str, jvmref, mkfs(class, ty, fieldvar) ', st0) ⊦ ty = void_type, jvmref ∈ st, (is_reftype(ty) → validrefval(str, (st ∪ st0)[jvmref -- mkfs(class, ty, fieldvar) '], ty, st ∪ st0)) ∧ type∃(str, ty) ∧ goodfieldandtype(jvmref, mkfs(class, ty, fieldvar) ', st ∪ st0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ 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 11:
tdname∃(str, class), mkfs(class, ty, fieldvar) ' ∈ statfields(class), initdone(class, st0), goodfieldandtype(jvmref, mkfs(class, ty, fieldvar) ', st0) ∧ 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, st0[jvmref -- mkfs(class, ty, fieldvar) '], mkfs(class, ty, fieldvar) ' .fs .type, st0)) ⊦ ty = void_type, jvmref ∈ st, (is_reftype(ty) → validrefval(str, (st ∪ st0)[jvmref -- mkfs(class, ty, fieldvar) '], ty, st ∪ st0)) ∧ type∃(str, ty) ∧ goodfieldandtype(jvmref, mkfs(class, ty, fieldvar) ', st ∪ st0)

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: validfield-def antecedent: succedent: 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)) substlist: [st, sk, r, str] → [st0, mkfs(class, ty, fieldvar) ', jvmref, str] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((0, 0, 3)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st0, mkfs(class, ty, fieldvar) ', jvmref, str)]]