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Proof step 6 from proof addobj-union-switch (previous step)

∀ r, r0, class, fis, st. r = r0 ∨ addobj(r, class, fis, update(r0, fis1, st)) = update(r0, fis1, addobj(r, class, fis, st)) ⊦ r = r0, addobj(r, class, fis, update(r0, fis1, st)[r0 -- sk, val]) = (update(r0, fis1, addobj(r, class, fis, st))[r0 -- sk, val])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ r ≠ r0 → addobj(r, class1, fis, st[r0 -- sk, val]) = (addobj(r, class1, fis, st)[r0 -- sk, val])
Proof step 5:
r ≠ r0, ∀ r, r0, class, fis, st. r = r0 ∨ addobj(r, class, fis, update(r0, fis1, st)) = update(r0, fis1, addobj(r, class, fis, st)) ⊦ r = r0, (addobj(r, class, fis, update(r0, fis1, st))[r0 -- sk, val]) = (update(r0, fis1, addobj(r, class, fis, st))[r0 -- sk, val])

Rule argument

[crewrite-arg: addobj-put-switch , F , [val, sk, r0, st, fis, class1, r] → [val, sk, r0, update(r0, fis1, st), fis, class, r] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (val, sk, r0, update(r0, fis1, st), fis, class, r)]]