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Proof step 29 from proof ac-mode-01 (previous step)

⊦ (addclass(class, fis, st)[_mode]) = st[_mode], mkfs(`java.lang.Object' .class, void_type, `mode' .field) ' ∈ fis

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 28:
∀ class, st. (addclass(class, fis0, st)[_mode]) = st[_mode] ∨ mkfs(`java.lang.Object' .class, void_type, `mode' .field) ' ∈ fis0 ⊦ (addclass(class, fv + fis0, st)[_mode]) = st[_mode], mkfs(`java.lang.Object' .class, void_type, `mode' .field) ' ∈ fv + fis0

Rule argument

[VARWITHVARSEQSARG : fis, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : fieldinits generated by [], +;], [CSIMPSEQ : ⊦ (st[rk0, val][rk]) = ((rk = rk0 ⊃ val; st[rk]))], [CSIMPSEQ : ⊦ _mode = jvmref -- sk ↔ sk = mkfs (`java.lang.Object' .class, void_type, `mode' .field) '], [CSIMPSEQ : ⊦ fs ' = fs0 ' ↔ fs = fs0], [CSIMPSEQ : ⊦ mkfs(class1, ty, fieldvar) = mkfs(class2, ty0, fieldvar0) ↔ ¬ ¬ ( class1 = class2 ∧ ty = ty0 ∧ fieldvar = fieldvar0)], [CSIMPSEQ : ⊦ stringvar .field = stringvar0 .field ↔ stringvar = stringvar0])]]