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Proof step 79 from proof compat-addclass (previous step)

fis .keys = statfields(class1), jvmref -- mkfs(class1, ty, fieldvar) ' ∈ st, initdone(class0, addclass(class1, fis, st)), okfieldinits(class1, fis), compatrefs(str, st), compatmode(str, st), initdone(class0, st), mkfs(class1, ty, fieldvar) ' ∈ statfields(class0), jvmref ∈ st, compat(str, st[jvmref -- mkfs(class1, ty, fieldvar) '], ty, st), class∃(str, class0) ∨ interface∃(str, class0), ∀ sk. sk ∈ statfields(class0) → jvmref -- sk ∈ st ∧ is_fskey(sk) ∧ compat(str, st[jvmref -- sk], sk .fs .type, st) ⊦ class1 = class0, compat(str, addclass(class1, fis, st)[jvmref -- mkfs(class1, ty, fieldvar) '], ty, addclass(class1, fis, st))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 63:
⊦ ¬ sk ∈ fis ∧ sk ≠ mkfs(class, void_type, `initstate' .field) ' → (addclass(class, fis, st)[r -- sk]) = st[r -- sk]
Proof step 77:
¬ (¬ mkfs(class1, ty, fieldvar) ' ∈ fis ∧ mkfs(class1, ty, fieldvar) ' ≠ mkfs(class1, void_type, `initstate' .field) '), fis .keys = statfields(class1), jvmref -- mkfs(class1, ty, fieldvar) ' ∈ st, initdone(class0, addclass(class1, fis, st)), okfieldinits(class1, fis), compatrefs(str, st), compatmode(str, st), initdone(class0, st), mkfs(class1, ty, fieldvar) ' ∈ statfields(class0), jvmref ∈ st, compat(str, st[jvmref -- mkfs(class1, ty, fieldvar) '], ty, st), class∃(str, class0) ∨ interface∃(str, class0), ∀ sk. sk ∈ statfields(class0) → jvmref -- sk ∈ st ∧ is_fskey(sk) ∧ compat(str, st[jvmref -- sk], sk .fs .type, st) ⊦ class1 = class0, compat(str, addclass(class1, fis, st)[jvmref -- mkfs(class1, ty, fieldvar) '], ty, addclass(class1, fis, st))
Proof step 78:
⊦ fis .keys = statfields(class) ∧ okfieldinits(class, fis) ∧ compat(str, val, ty, st) → compat(str, val, ty, addclass(class, 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(class1, ty, fieldvar) ', jvmref, st, fis, class1] ,F ,addfuns , ,ac-lookup-06 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ fs ' = fs0 ' ↔ fs = fs0], [CSIMPSEQ : ⊦ mkfs(class1, ty, fieldvar) = mkfs(class2, ty0, fieldvar0) ↔ ¬ ¬ ( class1 = class2 ∧ ty = ty0 ∧ fieldvar = fieldvar0)], [CSIMPSEQ : class1 ≠ class2, class2 ≠ `java.lang.Object' .class ⊦ initdone (class1, addclass(class2, fis, st)) ↔ initdone(class1, st)])], [EXTRATERMS : (mkfs(class1, ty, fieldvar) ', jvmref, st, fis, class1)]]