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Proof step 21 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), sk ∈ fis

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ ¬ sk ∈ fis → addobj(r, class1, fis + (sk × val) ' + fis0, st) = (addobj(r, class1, fis + fis0, st)[r -- sk, val])
Proof step 20:
¬ 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 + fis1, st)[r -- sk, val]), sk ∈ fis

Rule argument

[crewrite-arg: add-nput-01 , F , [st, fis0, val, sk, fis, class1, r] → [st, fis1, val, sk, fis, class, r] ]

Additional information

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