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Proof step 33 from proof path-dups (previous step)

(r ' + x1)[m] = (r ' + x1)[n], n < m, path(r ' + x1, H), m ≤ # x1, n < # x1 ⊦ m = n, x1 = [], n = 0, reachable-n(H, n, r, (r ' + x1)[n]), path(r ' + firstn(n, x1), H) ∧ x1[n - 1] = (r ' + x1)[n]

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 32:
n = m0 + 1, (r ' + x1)[m] = (r ' + x1)[n], n < m, path(r ' + x1, H), m ≤ # x1, n < # x1 ⊦ m = n, x1 = [], n = 0, reachable-n(H, n, r, (r ' + x1)[n]), path(r ' + firstn(n, x1), H) ∧ x1[m0] = (r ' + x1)[n]

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] → [n, 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 : (n, m0)]]