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Proof step 7 from proof put-last-rec (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ sks ≠ [] → st[r -- (sk ' + sks)] = st[st[r -- sk] .refval -- sks]
Proof step 6:
sks0 ≠ [], ∀ st, r, sk, val. st[r -- (sks0 + sk '), val] = st[st[r -- sks0] .refval -- sk, val] ⊦ st[st[r -- sk0] .refval -- (sks0 + sk '), val] = st[st[st[r -- sk0] .refval -- sks0] .refval -- sk, val], sks0 = []

Rule argument

[crewrite-arg: lookup-rec-01 , F , [sks, sk, r, st] → [sks0, sk0, r, st] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (sks0, sk0, r, st)]]