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Proof step 29 from proof validstatfields-addclass (previous step)

fis .keys = statfields(class0), validfieldinits(str, fis, st), tdname∃(str, class0), mkfs(class0, ty, fieldvar) ' ∈ statfields(class0), initdone(class0, addclass(class0, fis, st)) ⊦ class0 = `java.lang.Object' .class, is_fskey(mkfs(class0, ty, fieldvar) ') ∧ jvmref -- mkfs(class0, ty, fieldvar) ' ∈ addclass(class0, fis, st) ∧ okval(addclass(class0, fis, st)[jvmref -- mkfs(class0, ty, fieldvar) '], mkfs(class0, ty, fieldvar) ' .fs .type) ∧ type∃(str, mkfs(class0, ty, fieldvar) ' .fs .type) ∧ mkfs(class0, ty, fieldvar) ' .fs .type ≠ void_type ∧ ( is_reftype(mkfs(class0, ty, fieldvar) ' .fs .type) → validrefval (str, addclass(class0, fis, st)[jvmref -- mkfs(class0, ty, fieldvar) '], mkfs(class0, ty, fieldvar) ' .fs .type, addclass(class0, fis, st)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ validfieldinits(str, fis, st) ↔ (∀ sk, val. sk × val ∈ fis → is_fskey(sk) ∧ type∃(str, sk .fs .type) ∧ validval(str, val, sk .fs .type, st))
Proof step 28:
fis .keys = statfields(class0), ∀ sk, val. sk × val ∈ fis → is_fskey(sk) ∧ type∃(str, sk .fs .type) ∧ validval(str, val, sk .fs .type, st), tdname∃(str, class0), mkfs(class0, ty, fieldvar) ' ∈ statfields(class0), initdone(class0, addclass(class0, fis, st)) ⊦ class0 = `java.lang.Object' .class, is_fskey(mkfs(class0, ty, fieldvar) ') ∧ jvmref -- mkfs(class0, ty, fieldvar) ' ∈ addclass(class0, fis, st) ∧ okval(addclass(class0, fis, st)[jvmref -- mkfs(class0, ty, fieldvar) '], mkfs(class0, ty, fieldvar) ' .fs .type) ∧ type∃(str, mkfs(class0, ty, fieldvar) ' .fs .type) ∧ mkfs(class0, ty, fieldvar) ' .fs .type ≠ void_type ∧ ( is_reftype(mkfs(class0, ty, fieldvar) ' .fs .type) → validrefval (str, addclass(class0, fis, st)[jvmref -- mkfs(class0, ty, fieldvar) '], mkfs(class0, ty, fieldvar) ' .fs .type, addclass(class0, fis, st)))

Rule argument

[crewrite-arg: validfieldinits-def , F , [st, fis, str] → [st, fis, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, fis, str)]]