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Proof step 9 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 -- fv .1, fv .2]) = update(r0, fv ' + fis1, addobj(r, class, fis, st))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 8:
fv = sk × val, ∀ 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, fv ' + fis1, addobj(r, class, fis, st))

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)]]