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Proof step 28 from proof validstatfields-addclass (previous step)

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 7:
mkfs(class1, ty, fieldvar) ' ∈ fis ⊦ (addclass(class1, fis, st)[jvmref -- mkfs(class1, ty, fieldvar) ']) = fis[mkfs(class1, ty, fieldvar) ']
Proof step 13:
¬ 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)))
Proof step 27:
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(fis[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, fis[mkfs(class0, ty, fieldvar) '], mkfs(class0, ty, fieldvar) ' .fs .type, addclass(class0, fis, st)))

Rule argument

[speclemmaarg: mkfs(class1, ty, fieldvar) ' ∈ fis , (addclass(class1, fis, st)[jvmref -- mkfs(class1, ty, fieldvar) ']) = fis[mkfs(class1, ty, fieldvar) '] ,[fieldvar, ty, st, fis, class1] → [fieldvar, ty, st, fis, class0] ,F ,addfuns , ,ac-lookup ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (fieldvar, ty, st, fis, class0)]]