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Proof step 56 from proof path-dups (previous step)

(r ' + x1)[m] = x2 .last, (r ' + x1)[# x2] = x2 .last, path(r ' + x2, H), reachable-n(H, # x2, r, x2 .last), # x2 < m, # x2 < # x1, m ≤ # x1, path(r ' + x1, H) ⊦ x1 = [], x2 = [], ∃ x. path(x, H) ∧ hd x = r ∧ x .last = x2 .last ∧ # x = m + 1

User applied rule exists right

And obtained the following new goals

Proof step 55:
(r ' + x1)[m] = x2 .last, (r ' + x1)[# x2] = x2 .last, path(r ' + x2, H), reachable-n(H, # x2, r, x2 .last), # x2 < m, # x2 < # x1, m ≤ # x1, path(r ' + x1, H) ⊦ x1 = [], x2 = [], path(firstn(m + 1, r ' + x1), H) ∧ hd firstn(m + 1, r ' + x1) = r ∧ firstn(m + 1, r ' + x1) .last = x2 .last ∧ # firstn(m + 1, r ' + x1) = m + 1

Rule argument

[EXRARG : pos: right 3, [extquanttermlist: (firstn(m + 1, r ' + x1)) abort:F , discard:T , computed:F ]]

Additional information

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