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Proof step 10 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, sk0 ' + sks0, st)[r -- sk]) = st[r -- sk]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ addobj(r, class, sk ' + sks, st) = (addobj(r, class, sks, st)[r -- sk, initial_value(sk .fs .type)])
Proof step 9:
∀ 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]

Rule argument

[crewrite-arg: addobj-keysrec , F , [st, sks, sk, class, r] → [st, sks0, sk0, class, r0] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, sks0, sk0, class, r0)]]