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Proof step 9 from proof addobj-at-01 (previous step)

∀ 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 ⊦ (addobj(r0, class, sks0, st)[r0 -- sk0, initial_value(sk0 .fs .type)][r -- sk]) = st[r -- sk]

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 8:
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 ⊦ (addobj(r0, class, sks0, st)[r0 -- sk0, initial_value(ty)][r -- sk]) = st[r -- sk]

Rule argument

[speclemmaarg: , class = fs .class ∧ ty = fs .type ∧ fieldvar = fs .field ↔ fs = mkfs(class, ty, fieldvar) ,[fs, class, ty, fieldvar] → [sk0 .fs, class0, ty, fieldvar] ,T ,fieldspec , ,elim ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ class = fs .class ∧ ty = fs .type ∧ fieldvar = fs .field ↔ fs = mkfs(class, ty, fieldvar)])], [EXTRATERMS : (sk0 .fs, class0, ty, fieldvar)]]