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Proof step 8 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, fv ' + fis0, st[r -- _type, typeval(mkclasstype(class))]) = (addobj(r, class, fis0, st)[r -- fv .1, fv .2])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 7:
fv = sk × val, ∀ r, st, class. update(r, fis0, st[r -- _type, typeval(mkclasstype(class))]) = addobj(r, class, fis0, st) ⊦ update(r, fv ' + fis0, st[r -- _type, typeval(mkclasstype(class))]) = (addobj(r, class, fis0, st)[r -- sk, val])

Rule argument

[speclemmaarg: ,sk = fv .1 ∧ val = fv .2 ↔ fv = sk × val ,[fv, sk, val] → [fv, sk, val] ,T ,pair ,fieldinit ,elim ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ sk = fv .1 ∧ val = fv .2 ↔ fv = sk × val])], [EXTRATERMS : (fv, sk, val)]]