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Proof step 27 from proof lookup-put-ex-first (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Rule argument

[x0lemmaarg: spec-name: list-data instance-name: storekeys lemma-name: elim-list-c antecedent: sks ≠ [] succedent: sk = sks .first ∧ sks0 = sks .rest ↔ sks = sk + sks0 substlist: [sks, sk, sks0] → [sks0, sk1, sks4] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: T replace all?: T paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : sks ≠ [] ⊦ sk = sks .first ∧ sks0 = sks .rest ↔ sks = sk + sks0])], [EXTRATERMS : (sks0, sk1, sks4)]]