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Proof step 6 from proof ac-mode (previous step)

sk = fs ', fs = mkfs(class1, ty, fieldvar), is_fskey(sk), ∀ class1, st. class1 = `java.lang.Object' .class ∨ (addclass(class1, fis0, st)[_mode]) = st[_mode] ⊦ (addclass(class1, (sk × val) ' + fis0, st)[_mode]) = st[_mode], class1 = `java.lang.Object' .class

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
⊦ addclass(class1, (mkfs(class1, ty, fieldvar) ' × val) ' + fis, st) = (addclass(class1, fis, st)[jvmref -- mkfs(class1, ty, fieldvar) ', val])
Proof step 5:
∀ class1, st. class1 = `java.lang.Object' .class ∨ (addclass(class1, fis0, st)[_mode]) = st[_mode] ⊦ class1 = `java.lang.Object' .class, (addclass(class1, fis0, st)[_mode]) = st[_mode]

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_fskey(fs ')], [CSIMPSEQ : ⊦ mkfs(class1, ty, fieldvar) = mkfs(class2, ty0, fieldvar0) ↔ ¬ ¬ ( class1 = class2 ∧ ty = ty0 ∧ fieldvar = fieldvar0)], [CSIMPSEQ : ⊦ fs ' = fs0 ' ↔ fs = fs0], [CSIMPSEQ : ⊦ _mode = jvmref -- sk ↔ sk = mkfs (`java.lang.Object' .class, void_type, `mode' .field) '], [CSIMPSEQ : ⊦ (st[rk0, val][rk]) = ((rk = rk0 ⊃ val; st[rk]))], [CSIMPSEQ : ⊦ (fis + fis0) + fis1 = fis + fis0 + fis1])]]