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Proof step 31 from proof ac-lookup (conclusion)

mkfs(class1, ty, fieldvar) ' ∈ fis ⊦ (addclass(class1, fis, st)[jvmref -- mkfs(class1, ty, fieldvar) ']) = fis[mkfs(class1, ty, fieldvar) ']

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 30:
∀ class1, ty, fieldvar, st. mkfs(class1, ty, fieldvar) ' ∈ fis0 → (addclass(class1, fis0, st)[jvmref -- mkfs(class1, ty, fieldvar) ']) = fis0[mkfs(class1, ty, fieldvar) '] ⊦ mkfs(class1, ty, fieldvar) ' ∈ fv + fis0 → (addclass(class1, fv + fis0, st)[jvmref -- mkfs(class1, ty, fieldvar) ']) = (fv + fis0)[mkfs(class1, ty, fieldvar) ']

Rule argument

[VARWITHFMAVARSARG : fis, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : fieldinits generated by [], +;], [CSIMPSEQ : ⊦ (st[rk0, val][rk]) = ((rk = rk0 ⊃ val; st[rk]))], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ ¬ ¬ (r = r0 ∧ sk = sk0)], [CSIMPSEQ : ⊦ fs ' = fs0 ' ↔ fs = fs0], [CSIMPSEQ : ⊦ mkfs(class1, ty, fieldvar) = mkfs(class2, ty0, fieldvar0) ↔ ¬ ¬ ( class1 = class2 ∧ ty = ty0 ∧ fieldvar = fieldvar0)], [CSIMPSEQ : ⊦ ¬ sk ∈ []])]]