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Proof step 37 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) ∧ (r ' + firstn(n, x1)) .last = (r ' + x1)[n]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 25:
⊦ x0 ≠ [] → (r ' + x0) .last = x0 .last
Proof step 36:
firstn(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) ∧ firstn(n, x1) .last = (r ' + x1)[n]

Rule argument

[x0lemmaarg: spec-name: list-last instance-name: reflist lemma-name: l-02 antecedent: succedent: x0 ≠ [] → (r ' + x0) .last = x0 .last substlist: [x0, r] → [firstn(n, x1), r] 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 : ⊦ firstn(n, x0) = [] ↔ n = 0])], [EXTRATERMS : (firstn(n, x1), r)]]