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Proof step 18 from proof path-dups (previous step)

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

User applied rule all left

And obtained the following new goals

Proof step 17:
(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)

Rule argument

[EXRARG : pos: left 4, [extquanttermlist: (firstn(m + 1, r ' + x1)) abort:F , discard:T , computed:F ]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (firstn(m + 1, r ' + x1))]]