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Proof step 35 from proof path-dups (previous step)

(r ' + x1)[m] = (r ' + x1)[n], n < m, path(r ' + x1, H), m ≤ # x1, n < # x1 ⊦ n = 0, m = n, x1 = [], reachable-n(H, n, r, (r ' + x1)[n]), path(r ' + firstn(n, x1), H) ∧ firstn(n, x1) .last = (r ' + x1)[n]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 26:
⊦ m ≠ 0 ∧ m ≤ # x0 → firstn(m, x0) .last = x0[m -1]
Proof step 34:
n ≠ 0 ∧ n ≤ # x1, (r ' + x1)[m] = (r ' + x1)[n], n < m, path(r ' + x1, H), m ≤ # x1, n < # x1 ⊦ n = 0, m = n, x1 = [], reachable-n(H, n, r, (r ' + x1)[n]), path(r ' + firstn(n, x1), H) ∧ x1[n -1] = (r ' + x1)[n]

Rule argument

[x0lemmaarg: spec-name: list-del instance-name: reflist lemma-name: firstn-last antecedent: succedent: m ≠ 0 ∧ m ≤ # x0 → firstn(m, x0) .last = x0[m -1] substlist: [x0, m] → [x1, n] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((1, 0, 4, 1, 1, 1, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m < n → m ≤ n])], [EXTRATERMS : (x1, n)]]