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Proof step 27 from proof ac-in-10 (conclusion)

⊦ ¬ sk ∈ fis ∧ sk ≠ mkfs(class, void_type, `initstate' .field) ' → (r -- sk ∈ addclass(class, fis, st) ↔ r -- sk ∈ st)

User applied rule structural induction

And obtained the following new goals

Proof step 1:
⊦ addclass(class1, [], st) = st[jvmref -- mkfs(class1, void_type, `initstate' .field) ', initval(done)]
Proof step 26:
∀ sk, class, r, st. ¬ sk ∈ fis0 ∧ sk ≠ mkfs(class, void_type, `initstate' .field) ' → (r -- sk ∈ addclass(class, fis0, st) ↔ r -- sk ∈ st) ⊦ ¬ sk ∈ fv + fis0 ∧ sk ≠ mkfs(class, void_type, `initstate' .field) ' → (r -- sk ∈ addclass(class, fv + fis0, st) ↔ r -- sk ∈ st)

Rule argument

[VARWITHVARSEQSARG : fis, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : fieldinits generated by [], +;], [CSIMPSEQ : ⊦ rk ∈ st[rk0, val] ↔ rk = rk0 ∨ rk ∈ st], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ ¬ ¬ (r = r0 ∧ sk = sk0)])]]