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Proof step 11 from proof lookup-list-intro-02 (previous step)

∀ sks0, st, r. sks0 = [] ∨ st[st[r -- sks1] .refval -- sks0] = st[r -- (sks1 + sks0)] ⊦ sks1 = [], sks0 = [], st[st[r -- (sk ' + sks1)] .refval -- sks0] = st[r -- ((sk ' + sks1) + sks0)]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ sks ≠ [] → st[r -- (sk ' + sks)] = st[st[r -- sk] .refval -- sks]
Proof step 10:
sks1 ≠ [], ∀ sks0, st, r. sks0 = [] ∨ st[st[r -- sks1] .refval -- sks0] = st[r -- (sks1 + sks0)] ⊦ sks1 = [], sks0 = [], st[st[st[r -- sk] .refval -- sks1] .refval -- sks0] = st[r -- ((sk ' + sks1) + sks0)]

Rule argument

[crewrite-arg: lookup-rec-01, F, [sks, sk, r, st] → [sks1, sk, r, st]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (sks1, sk, r, st)]]