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Proof step 23 from proof add-update-same (previous step)

∀ r, fis, class, st. update(r, fis, addobj(r, class, fis1, st)) = addobj(r, class, fis + fis1, st) ⊦ update(r, fis, addobj(r, class, fis1, st)[r -- sk, val]) = addobj(r, class, fis + (sk × val) ' + fis1, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ ¬ sk ∈ fis → update(r, fis, st[r -- sk, val]) = (update(r, fis, st)[r -- sk, val])
Proof step 17:
¬ ¬ sk ∈ fis, ∀ r, fis, class, st. update(r, fis, addobj(r, class, fis1, st)) = addobj(r, class, fis + fis1, st) ⊦ update(r, fis, addobj(r, class, fis1, st)[r -- sk, val]) = addobj(r, class, fis + (sk × val) ' + fis1, st)
Proof step 22:
¬ sk ∈ fis, ∀ r, fis, class, st. update(r, fis, addobj(r, class, fis1, st)) = addobj(r, class, fis + fis1, st) ⊦ (update(r, fis, addobj(r, class, fis1, st))[r -- sk, val]) = addobj(r, class, fis + (sk × val) ' + fis1, st)

Rule argument

[speclemmaarg: , ¬ sk ∈ fis → update(r, fis, st[r -- sk, val]) = (update(r, fis, st)[r -- sk, val]) ,[val, sk, st, fis, r] → [val, sk, addobj(r, class, fis1, st), fis, r] ,F ,okfuns , ,update-put-rew ]

Additional information

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