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Proof step 3 from proof ac-one1 (conclusion)

⊦ addclass(class1, (mkfs(class1, ty, fieldvar) ' × val) ', st) = (st[jvmref -- mkfs(class1, void_type, `initstate' .field) ', initval(done)][jvmref -- mkfs(class1, ty, fieldvar) ', val])

User applied rule insert lemma

And obtained the following new goals

Proof step 1:
⊦ addclass(class1, (mkfs(class1, ty, fieldvar) ' × val) ' + fis, st) = (addclass(class1, fis, st)[jvmref -- mkfs(class1, ty, fieldvar) ', val])
Proof step 2:
⊦ addclass(class1, [], st) = st[jvmref -- mkfs(class1, void_type, `initstate' .field) ', initval(done)]

Rule argument

[LEMMAARG : addclass-yes, [class1, ty, fieldvar, val, fis, st] → [class1, ty, fieldvar, val, [], st]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ fis + [] = fis], [CSIMPSEQ : ⊦ (fis + fis0) + fis1 = fis + fis0 + fis1])], [EXTRATERMS : (class1, ty, fieldvar, val, [], st)]]