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Proof step 25 from proof lookup-put-ex-first (previous step)

st[r -- (sk0 ' + sks4)] .refval = st[st[r -- sk0] .refval -- sks] .refval, sks4 + sk ' ⊑ sks, r ≠ st[st[r -- sk] .refval -- sks] .refval ∨ sk0 ≠ sk ⊦ st[st[r -- sk0] .refval -- sks4] .refval = st[r -- (sk0 ' + sks4)] .refval, (st[st[r -- (sk0 ' + sks4)] .refval -- sk, val][st[r -- sk0] .refval -- (sks + sk ' + sks1)]) = st[st[r -- sk0] .refval -- (sks + sk ' + sks1)], sks = [], ∃ sks0, sks2. sk0 ' + sks + sk ' + sks1 = sks0 + sk ' + sks2 ∧ st[r -- sks0] .refval = st[r -- (sk0 ' + sks4)] .refval ∧ (∀ 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: instance-name: lemma-name: lookup-rec-01 antecedent: succedent: sks ≠ [] → st[r -- (sk ' + sks)] = st[st[r -- sk] .refval -- sks] substlist: [sks, sk, r, st] → [sks4, sk0, r, st] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((1, 0, 0, 1, 1, 1, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : list, storekeys, app, ⊦ sks + [] = sks], [CSIMPNAMEDSEQ : list, storekeys, a, ⊦ (sks + sks0) + sks1 = sks + sks0 + sks1], [CSIMPNAMEDSEQ : javavalue, , sel-09, ⊦ refval(r) .refval = r])], [EXTRATERMS : (sks4, sk0, r, st)]]