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Proof step 17 from proof path-dups (previous step)

(r ' + x1)[m] = r, path(r ' + x1, H), m ≤ # x1, ¬ path(firstn(m + 1, r ' + x1), H) ∨ hd firstn(m + 1, r ' + x1) ≠ firstn(m + 1, r ' + x1) .last ∨ firstn(m + 1, r ' + x1) .last ≠ r ∨ # firstn(m + 1, r ' + x1) ≠ m + 1 ⊦ x1 = [], m = 0, reachable-n(H, m, r, r)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
(r ' + x1)[m] = r, path(r ' + x1, H), m ≤ # x1, ¬ path(r ' + firstn(m, x1), H) ∨ (r ' + firstn(m, x1)) .last ≠ r ⊦ x1 = [], m = 0, reachable-n(H, m, r, r)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m + n = m + n0 ↔ n = n0], [CSIMPSEQ : ⊦ # firstn(n, x0) = n], [CSIMPSEQ : ⊦ # r ' = 0 +1], [CSIMPSEQ : ⊦ # (x0 + x1) = # x0 + # x1], [CSIMPSEQ : ⊦ hd (r ' + x0) = r], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ (x0 + x1) + x2 = x0 + x1 + x2], [CSIMPSEQ : ⊦ r + x0 = r ' + x0], [CSIMPSEQ : ⊦ firstn(n + 1, r ' + x0) = r + firstn(n, x0)])]]