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Proof step 14 from proof path-dups (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ m ≠ 0 ∧ m ≤ # x0 → firstn(m, x0) .last = x0[m -1]
Proof step 13:
m ≠ 0 ∧ m ≤ # x1, (r ' + x1)[m] = r, path(r ' + x1, H), m ≤ # x1, ¬ path(x1[m -1] ' + firstn(m, x1), H) ∨ x1[m -1] ≠ r ⊦ x1 = [], m = 0, reachable-n(H, m, r, r)

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, m] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 3, 1, 1, 1, 0, 1, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (x1, m)]]