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Proof step 3 from proof lookup-put-keys (previous step)

⊦ sk = sk0, sks0 = [], (st[r -- (sks + sk '), val][r0 -- (sk0 ' + sks0)]) = (st[r -- (sks + sk '), val][st[r0 -- sk0] .refval -- sks0])

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]
Proof step 2:
⊦ sk ≠ sk0 → (st[r -- (sks + sk '), val][r0 -- sk0]) = st[r0 -- sk0]

Rule argument

[crewrite-arg: lookup-rec-01 , F , [sks, sk, r, st] → [sks0, sk0, r0, st[r -- (sks + sk '), val]] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (sks + sks0) + sks1 = sks + sks0 + sks1])], [EXTRATERMS : (sks0, sk0, r0, st[r -- (sks + sk '), val])]]