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Proof step 6 from proof add-update-same (previous step)

∀ r, st, class. update(r, fis0, st[r -- _type, typeval(mkclasstype(class))]) = addobj(r, class, fis0, st) ⊦ update(r, (sk × val) ' + fis0, st[r -- _type, typeval(mkclasstype(class))]) = (addobj(r, class, fis0, st)[r -- sk, val])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ update(r, (sk × val) ' + fis, st) = (update(r, fis, st)[r -- sk, val])
Proof step 5:
∀ r, st, class. update(r, fis0, st[r -- _type, typeval(mkclasstype(class))]) = addobj(r, class, fis0, st) ⊦ (update(r, fis0, st[r -- _type, typeval(mkclasstype(class))])[r -- sk, val]) = (addobj(r, class, fis0, st)[r -- sk, val])

Rule argument

[speclemmaarg: , update(r, (sk × val) ' + fis, st) = (update(r, fis, st)[r -- sk, val]) ,[st, fis, val, sk, r] → [st[r -- _type, typeval(mkclasstype(class))], fis0, val, sk, r] ,F ,okfuns , ,update-rec ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st[r -- _type, typeval(mkclasstype(class))], fis0, val, sk, r)]]