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Proof step 34 from proof addobj-addclass-sw (previous step)

⊦ jvmref = r, ( jvmref -- mkfs(class1, ty, fieldvar) ' ∈ addclass(class0, fis0, st) ↔ jvmref -- mkfs(class1, ty, fieldvar) ' ∈ addclass(class0, fis0, addobj(r, class, fis, st))) ∧ (addclass(class0, fis0, st)[jvmref -- mkfs(class1, ty, fieldvar) ']) = (addclass(class0, fis0, addobj(r, class, fis, st))[jvmref -- mkfs(class1, ty, fieldvar) ']), ¬ mkfs(class1, ty, fieldvar) ' ∈ fis0 ∧ (class1 ≠ class0 ∨ ty ≠ void_type ∨ fieldvar ≠ `initstate' .field)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 25:
class1 ≠ class2 ⊦ (addclass(class2, fis, st)[jvmref -- mkfs(class1, ty, fieldvar) ']) = st[jvmref -- mkfs(class1, ty, fieldvar) ']
Proof step 26:
⊦ 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))
Proof step 27:
⊦ r ≠ r0 → (r -- sk ∈ addobj(r0, class1, fis, st) ↔ r -- sk ∈ st)
Proof step 28:
mkfs(class1, ty, fieldvar) ' ∈ fis ⊦ (addclass(class1, fis, st)[jvmref -- mkfs(class1, ty, fieldvar) ']) = fis[mkfs(class1, ty, fieldvar) ']
Proof step 29:
¬ mkfs(class1, void_type, `initstate' .field) ' ∈ fis ⊦ (addclass(class1, fis, st)[jvmref -- mkfs(class1, void_type, `initstate' .field) ']) = initval(done)
Proof step 30:
class1 ≠ class2 ⊦ jvmref -- mkfs(class2, ty, fieldvar) ' ∈ addclass(class1, fis, st) ↔ jvmref -- mkfs(class2, ty, fieldvar) ' ∈ st
Proof step 31:
⊦ r ≠ r0 → (r -- sk ∈ addobj(r0, class1, fis, st) ↔ r -- sk ∈ st)
Proof step 32:
class1 ≠ class2 ⊦ (addclass(class2, fis, st)[jvmref -- mkfs(class1, ty, fieldvar) ']) = st[jvmref -- mkfs(class1, ty, fieldvar) ']
Proof step 33:
⊦ r ≠ r0 → (addobj(r, class1, fis, st)[r0 -- sk]) = st[r0 -- sk]

Rule argument

[crewrite-arg: ac-lookup-02 , F , [fieldvar, ty, class1, st, fis, class2] → [fieldvar, ty, class1, addobj(r, class, fis, st), fis0, class0] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ mkfs(class, ty, fieldvar) = mkfs(class0, ty0, fieldvar0) ↔ class = class0 ∧ ty = ty0 ∧ fieldvar = fieldvar0], [CSIMPSEQ : ⊦ mkfs(class1, ty, fieldvar) = mkfs(class2, ty0, fieldvar0) ↔ ¬ ¬ ( class1 = class2 ∧ ty = ty0 ∧ fieldvar = fieldvar0)], [CSIMPSEQ : ⊦ initval(istate) = initval(istate0) ↔ istate = istate0])], [EXTRATERMS : (fieldvar, ty, class1, addobj(r, class, fis, st), fis0, class0)]]