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Proof step 12 from proof path-dups (previous step)

(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)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 11:
m = m0 + 1, (r ' + x1)[m] = r, path(r ' + x1, H), m ≤ # x1, ¬ path(x1[m0] ' + firstn(m, x1), H) ∨ x1[m0] ≠ r ⊦ x1 = [], m = 0, reachable-n(H, m, r, r)

Rule argument

[x0lemmaarg: spec-name: nat instance-name: lemma-name: elim-pred-c antecedent: n ≠ 0 succedent: m = n - 1 ↔ n = m + 1 substlist: [n, m] → [m, m0] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: T replace all?: T paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1])], [EXTRATERMS : (m, m0)]]