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Proof step 13 from proof validstatfields-addclass (previous step)

¬ mkfs(class0, ty, fieldvar) ' ∈ fis, 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)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ ¬ sk ∈ fis ∧ sk ≠ mkfs(class, void_type, `initstate' .field) ' → (addclass(class, fis, st)[r -- sk]) = st[r -- sk]
Proof step 12:
¬ mkfs(class0, ty, fieldvar) ' ∈ fis ∧ mkfs(class0, ty, fieldvar) ' ≠ mkfs(class0, void_type, `initstate' .field) ', ¬ mkfs(class0, ty, fieldvar) ' ∈ fis, 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(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, st[jvmref -- mkfs(class0, ty, fieldvar) '], mkfs(class0, ty, fieldvar) ' .fs .type, addclass(class0, fis, st)))

Rule argument

[speclemmaarg: , ¬ sk ∈ fis ∧ sk ≠ mkfs(class, void_type, `initstate' .field) ' → (addclass(class, fis, st)[r -- sk]) = st[r -- sk] ,[sk, r, st, fis, class] → [mkfs(class0, ty, fieldvar) ', jvmref, st, fis, class0] ,F ,addfuns , ,ac-lookup-06 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_fskey(fs ')], [CSIMPSEQ : ⊦ fs ' .fs = fs], [CSIMPSEQ : ⊦ mkfs(class, ty, fieldvar) .type = ty], [CSIMPSEQ : ⊦ ¬ mkfs (class0, void_type, fieldvar) ' ∈ statfields(class)], [CSIMPSEQ : ⊦ fs ' = fs0 ' ↔ fs = fs0], [CSIMPSEQ : ⊦ mkfs(class, ty, fieldvar) = mkfs(class0, ty0, fieldvar0) ↔ class = class0 ∧ ty = ty0 ∧ fieldvar = fieldvar0])], [EXTRATERMS : (mkfs(class0, ty, fieldvar) ', jvmref, st, fis, class0)]]