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Proof step 2 from proof update-at-01 (previous step)

⊦ rk .ref = r0, (update(r0, fis, st)[rk]) = st[rk]

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 1:
⊦ r ≠ r0 → (update(r0, fis, st)[r -- sk]) = st[r -- sk]

Rule argument

[speclemmaarg: ,r = rk .ref ∧ sk = rk .key ↔ rk = r -- sk ,[rk, r, sk] → [rk, r, sk] ,T ,refkey , ,elim ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ r = rk .ref ∧ sk = rk .key ↔ rk = r -- sk])], [EXTRATERMS : (rk, r, sk)]]