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Proof step 6 from proof addobj-at-01 (previous step)

sk0 .fs = mkfs(class0, ty, fieldvar), ∀ r, r0, sk, class, st. r ≠ r0 ∨ ¬ sk ∈ sks0 ∧ sk ≠ _type → (addobj(r0, class, sks0, st)[r -- sk]) = st[r -- sk], r ≠ r0 ∨ sk ≠ sk0 ∧ ¬ sk ∈ sks0 ∧ sk ≠ _type, r ≠ r0 ∨ sk ≠ sk0 ⊦ (addobj(r0, class, sks0, st)[r0 -- sk0, initial_value(ty)][r -- sk]) = st[r -- sk]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ rk ≠ rk0 → (st[rk0, val][rk]) = st[rk]
Proof step 5:
r -- sk ≠ r0 -- sk0, sk0 .fs = mkfs(class0, ty, fieldvar), ∀ r, r0, sk, class, st. r ≠ r0 ∨ ¬ sk ∈ sks0 ∧ sk ≠ _type → (addobj(r0, class, sks0, st)[r -- sk]) = st[r -- sk], r ≠ r0 ∨ sk ≠ sk0 ∧ ¬ sk ∈ sks0 ∧ sk ≠ _type, r ≠ r0 ∨ sk ≠ sk0 ⊦ (addobj(r0, class, sks0, st)[r -- sk]) = st[r -- sk]

Rule argument

[speclemmaarg: ,rk ≠ rk0 → (st[rk0, val][rk]) = st[rk] ,[rk, val, rk0, st] → [r -- sk, initial_value(ty), r0 -- sk0, addobj(r0, class, sks0, st)] ,F ,store ,javastore ,At-other ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0])], [EXTRATERMS : (r -- sk, initial_value(ty), r0 -- sk0, addobj(r0, class, sks0, st))]]