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Proof step 10 from proof validstatfield-union (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ goodfieldandtype(r, sk, st) ↔ is_fskey(sk) ∧ r -- sk ∈ st ∧ okval(st[r -- sk], sk .fs .type)
Proof step 9:
tdname∃(str, class), mkfs(class, ty, fieldvar) ' ∈ statfields(class), initdone(class, st0), jvmref -- mkfs(class, ty, fieldvar) ' ∈ st0, okval(st0[jvmref -- mkfs(class, ty, fieldvar) '], ty), type∃(str, ty), jvmref ∈ st0, is_reftype(ty) → validrefval(str, st0[jvmref -- mkfs(class, ty, fieldvar) '], ty, st0) ⊦ ty = void_type, jvmref ∈ st, (is_reftype(ty) → validrefval(str, st0[jvmref -- mkfs(class, ty, fieldvar) '], ty, st ∪ st0)) ∧ is_fskey(mkfs(class, ty, fieldvar) ') ∧ jvmref -- mkfs(class, ty, fieldvar) ' ∈ st ∪ st0 ∧ okval((st ∪ st0)[jvmref -- mkfs(class, ty, fieldvar) '], mkfs(class, ty, fieldvar) ' .fs .type)

Rule argument

[x0lemmaarg: spec-name: okfuns instance-name: lemma-name: good-field-def antecedent: succedent: goodfieldandtype(r, sk, st) ↔ is_fskey(sk) ∧ r -- sk ∈ st ∧ okval(st[r -- sk], sk .fs .type) substlist: [st, sk, r] → [st ∪ st0, mkfs(class, ty, fieldvar) ', jvmref] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((1, 0, 2, 1, 1)) dummy: () ]

Additional information

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