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Proof step 14 from proof in-list-put (previous step)

⊦ sks = [], r -- sks ∈ st[rk, val] ↔ r -- sks ∈ st, rk .key ∈ sks

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 13:
rk = r0 -- sk ⊦ sks = [], r -- sks ∈ st[rk, val] ↔ r -- sks ∈ st, sk ∈ sks

Rule argument

[speclemmaarg: ,r = rk .ref ∧ sk = rk .key ↔ rk = r -- sk ,[rk, r, sk] → [rk, r0, sk] ,T ,refkey , ,elim ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ r = rk .ref ∧ sk = rk .key ↔ rk = r -- sk])], [EXTRATERMS : (rk, r0, sk)]]