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Proof step 2 from proof at-put-first-rec (previous step)

⊦ sk = sk0, sks = [], (st[r -- sk, val][r0 -- (sk0 ' + sks)]) = (st[r -- sk, val][st[r0 -- sk0] .refval -- sks])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ sks ≠ [] → st[r -- (sk ' + sks)] = st[st[r -- sk] .refval -- sks]

Rule argument

[crewrite-arg: lookup-rec-01 , F , [sks, sk, r, st] → [sks, sk0, r0, st[r -- sk, val]] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ sk ≠ sk0 → (st[r -- sk, val][r0 -- sk0]) = st[r0 -- sk0]])], [EXTRATERMS : (sks, sk0, r0, st[r -- sk, val])]]