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Proof step 11 from proof suffix-lcp (previous step)

ar[n0] = ar[n2], suffix(ar, n1) < suffix(ar, n2), suffix(ar, n0) < suffix(ar, n1), n2 < # ar, n1 ≤ # ar, n0 < # ar, (((n1 = # ar ∨ ar[n2] ≠ ar[n1]) ⊃ 0; lcp(ar, n0 + 1, n1 + 1) + 1)) ≤ lcp(ar, n0 + 1, n2 + 1), ∀ ar0, n, n3, n4. lcp(ar, n0 + 1, n2 + 1) ≠ lcp(ar0, n, n3) ∨ ¬ lcp(ar0, n, n4) < lcp(ar0, n, n3) ∨ ¬ suffix(ar0, n4) < suffix(ar0, n3) ∨ ¬ suffix(ar0, n) < suffix(ar0, n4) ∨ ¬ n3 ≤ # ar0 ∨ ¬ n4 ≤ # ar0 ∨ ¬ n ≤ # ar0 ⊦ n2 = # ar, n0 = # ar

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[x0lemmaarg: spec-name: suffix instance-name: lemma-name: lexicographic-suffix-next antecedent: succedent: n0 < # ar ∧ n1 < # ar → ( suffix(ar, n0) < suffix(ar, n1) ↔ ar[n0] < ar[n1] ∨ suffix(ar, n0 + 1) < suffix(ar, n1 + 1) ∧ ar[n0] = ar[n1]) substlist: [n1, n0, ar] → [n1, n0, ar] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 2)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ m < n ↔ n ≤ m], [CSIMPSEQ : ⊦ m ≤ n → (n ≤ m ↔ m = n)], [CSIMPSEQ : ⊦ 0 ≤ m], [CSIMPFORWARD : ⊦ m < n ∧ n = n0 → m < n0], [CSIMPSEQ : ⊦ m ≤ m], [CSIMPSEQ : ⊦ suffix(ar, # ar) = mkarray(0)], [CSIMPSEQ : ⊦ ar < mkarray(0) ↔ false])], [EXTRATERMS : (n1, n0, ar)]]