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Proof step 9 from proof lookup-last-rec (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
sks0 = [] ∨ (∀ st, r, sk. st[r -- (sks0 + sk ')] = st[st[r -- sks0] .refval -- sk]) ⊦ st[r -- ((sk0 ' + sks0) + sk ')] = st[st[r -- (sk0 ' + sks0)] .refval -- sk]

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (sks + sks0) + sks1 = sks + sks0 + sks1], [CSIMPSEQ : ⊦ sk ' + sks ≠ []], [CSIMPSEQ : ⊦ sk + sks = sk ' + sks])]]