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Proof step 10 from proof lookup-list-intro-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ sks ≠ [] → st[r -- (sk ' + sks)] = st[st[r -- sk] .refval -- sks]
Proof step 9:
sks0 + sk0 ' ≠ [], ∀ st, r, sk0. st[st[r -- sks0] .refval -- sk0] = st[r -- (sks0 + sk0 ')] ⊦ sks0 = [], st[st[st[r -- sk] .refval -- sks0] .refval -- sk0] = st[st[r -- sk] .refval -- (sks0 + sk0 ')]

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ sks + sks0 ≠ [] ↔ sks = [] ∧ sks0 = []], [CSIMPSEQ : ⊦ (sks + sks0) + sks1 = sks + sks0 + sks1])], [EXTRATERMS : (sks0 + sk0 ', sk, r, st)]]