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Proof step 20 from proof lookup-put-ex-first (previous step)

r = st[st[r -- sk0] .refval -- sks] .refval, sk ' ⊑ sk0 ' + sks, ∀ sks0. sks0 + sk ' ⊑ sks → st[st[r -- sk0] .refval -- sks0] .refval ≠ r ⊦ sks = [], (st[r -- sk, val][st[r -- sk0] .refval -- (sks + sk ' + sks1)]) = st[st[r -- sk0] .refval -- (sks + sk ' + sks1)], sk0 = sk, ∃ sks0, sks2. sk0 ' + sks + sk ' + sks1 = sks0 + sk ' + sks2 ∧ st[r -- sks0] .refval = r ∧ (∀ sks3. sks3 + sk ' ⊑ sks0 → st[r -- sks3] .refval ≠ st[r -- sks0] .refval)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[x0lemmaarg: spec-name: list-last instance-name: storekeys lemma-name: prefix-rec antecedent: succedent: sks ≠ [] → (sks ⊑ sk ' + sks0 ↔ sks .first = sk ∧ sks .rest ⊑ sks0) substlist: [sks0, sk, sks] → [sks, sk0, sk '] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 1)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : list, storekeys, first, ⊦ sk ' .first = sk], [CSIMPNAMEDSEQ : list, storekeys, e, ⊦ sk ' ≠ []])], [EXTRATERMS : (sks, sk0, sk ')]]