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Proof step 13 from proof path-dups (previous step)

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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
(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

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ n -1 = n - 1])]]