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Proof step 6 from proof at-put-last-other (previous step)

∀ r1, st0, r2, sk1, val0. r1 = st0[r2 -- sks0] .refval ∨ (st0[r2 -- (sks0 + sk1 '), val0][r1 -- sk1]) = st0[r1 -- sk1] ⊦ sks0 = [], (st[st[r -- sk] .refval -- (sks0 + sk0 '), val][st[st[r -- sk] .refval -- sks0] .refval -- sk0]) = st[st[st[r -- sk] .refval -- sks0] .refval -- sk0], st[st[r -- sk] .refval -- sks0] .refval = st[r -- (sk ' + sks0)] .refval

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]

Rule argument

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

Additional information

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