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Proof step 70 from proof validstatfield-putrkvs (previous step)

validvals(str, rkvs, st), 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, is_reftype(ty) → validrefval(str, st[jvmref -- mkfs(class, ty, fieldvar) '], ty, st) ⊦ ty = void_type, _uninit ∈ rkvs, jvmref -- mkfs(class, void_type, `initstate' .field) ' ∈ rkvs, (is_reftype(ty) → validrefval(str, st[rkvs][jvmref -- mkfs(class, ty, fieldvar) '], ty, st[rkvs])) ∧ goodfieldandtype(jvmref, mkfs(class, ty, fieldvar) ', st[rkvs])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ goodfieldandtype(r, sk, st) ↔ is_fskey(sk) ∧ r -- sk ∈ st ∧ okval(st[r -- sk], sk .fs .type)
Proof step 69:
validvals(str, rkvs, st), 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, is_reftype(ty) → validrefval(str, st[jvmref -- mkfs(class, ty, fieldvar) '], ty, st) ⊦ ty = void_type, _uninit ∈ rkvs, jvmref -- mkfs(class, void_type, `initstate' .field) ' ∈ rkvs, (is_reftype(ty) → validrefval(str, st[rkvs][jvmref -- mkfs(class, ty, fieldvar) '], ty, st[rkvs])) ∧ is_fskey(mkfs(class, ty, fieldvar) ') ∧ jvmref -- mkfs(class, ty, fieldvar) ' ∈ st[rkvs] ∧ okval(st[rkvs][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[rkvs], mkfs(class, ty, fieldvar) ', jvmref] ,F ,okfuns , ,good-field-def ]

Additional information

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