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Proof step 12 from proof ac-init-01 (previous step)

initundone(class, addclass(class, fis0, st)[jvmref -- mkfs(class, ty, fieldvar) ', val]), void_type ≠ ty ∨ `initstate' .field ≠ fieldvar ⊦ mkfs(class, void_type, `initstate' .field) ' ∈ fis0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ initundone(class1, st) ↔ (jvmref -- mkfs(class1, void_type, `initstate' .field) ') × initval(undone) ∈ st ∨ ¬ jvmref -- mkfs(class1, void_type, `initstate' .field) ' ∈ st ∧ _uninit ∈ st
Proof step 10:
¬ mkfs(class1, void_type, `initstate' .field) ' ∈ fis ⊦ (addclass(class1, fis, st)[jvmref -- mkfs(class1, void_type, `initstate' .field) ']) = initval(done)
Proof step 11:
⊦ jvmref -- mkfs(class1, ty, fieldvar) ' ∈ addclass(class1, fis, st) ↔ ¬ ¬ ( mkfs(class1, ty, fieldvar) ' ∈ fis ∨ jvmref -- mkfs(class1, ty, fieldvar) ' ∈ st ∨ mkfs(class1, ty, fieldvar) = mkfs(class1, void_type, `initstate' .field))

Rule argument

[speclemmaarg: , initundone(class1, st) ↔ (jvmref -- mkfs(class1, void_type, `initstate' .field) ') × initval(undone) ∈ st ∨ ¬ jvmref -- mkfs(class1, void_type, `initstate' .field) ' ∈ st ∧ _uninit ∈ st ,[st, class1] → [addclass(class, fis0, st) [jvmref -- mkfs(class, ty, fieldvar) ', val ], class] ,F ,storefuns , ,initundone ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ rk × val ∈ st ↔ rk ∈ st ∧ st[rk] = val], [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(class, ty, fieldvar) = mkfs(class0, ty0, fieldvar0) ↔ class = class0 ∧ ty = ty0 ∧ fieldvar = fieldvar0], [CSIMPSEQ : ⊦ rk ∈ st[rk0, val] ↔ rk = rk0 ∨ rk ∈ st], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ ¬ ¬ (r = r0 ∧ sk = sk0)], [CSIMPSEQ : ⊦ mkfs(class1, ty, fieldvar) = mkfs(class2, ty0, fieldvar0) ↔ ¬ ¬ ( class1 = class2 ∧ ty = ty0 ∧ fieldvar = fieldvar0)], [CSIMPSEQ : ⊦ initval(istate) = initval(istate0) ↔ istate = istate0], [CSIMPSEQ : ⊦ done ≠ undone])], [EXTRATERMS : (addclass(class, fis0, st) [jvmref -- mkfs(class, ty, fieldvar) ', val ], class)]]