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Proof step 8 from proof ac-mode-01 (previous step)

sk = fs ', fs = mkfs(class, ty, fieldvar), is_fskey(sk), ∀ class0, st0. (addclass(class0, fis0, st0)[_mode]) = st0[_mode] ⊦ mkfs(`java.lang.Object' .class, void_type, `mode' .field) ' = sk, (addclass(class, (sk × val) ' + fis0, st)[_mode]) = st[_mode], mkfs(`java.lang.Object' .class, void_type, `mode' .field) ' ∈ fis0

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 ≠ `java.lang.Object' .class ⊦ (addclass(class1, fis, st)[_mode]) = st[_mode]
Proof step 7:
`mode' .field ≠ fieldvar ∨ void_type ≠ ty, ∀ class0, st0. (addclass(class0, fis0, st0)[_mode]) = st0[_mode] ⊦ (((ty = void_type ∧ fieldvar = `mode' .field) ⊃ val; addclass(`java.lang.Object' .class, fis0, st)[_mode])) = st[_mode], mkfs(`java.lang.Object' .class, void_type, `mode' .field) ' ∈ fis0

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_fskey(fs ')], [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], [CSIMPSEQ : ⊦ mkfs(class1, ty, fieldvar) = mkfs(class2, ty0, fieldvar0) ↔ ¬ ¬ ( class1 = class2 ∧ ty = ty0 ∧ fieldvar = fieldvar0)], [CSIMPSEQ : ⊦ fs ' = fs0 ' ↔ fs = fs0])]]