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Proof step 7 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, (sk × val) ' + fis1, addobj(r, class, fis, st))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ update(r, (sk × val) ' + fis, st) = (update(r, fis, st)[r -- sk, val])
Proof step 6:
∀ 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

[speclemmaarg: , update(r, (sk × val) ' + fis, st) = (update(r, fis, st)[r -- sk, val]) ,[st, fis, val, sk, r] → [addobj(r, class, fis, st), fis1, val, sk, r0] ,F ,okfuns , ,update-rec ]

Additional information

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