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Proof step 19 from proof path-dups (previous step)

m ≠ 0 → (reachable-n(H, m, r, r) ↔ (∃ x. path(x, H) ∧ hd x = r ∧ x .last = r ∧ # x = m + 1)), (r ' + x1)[m] = r, path(r ' + x1, H), m ≤ # x1 ⊦ x1 = [], m = 0, reachable-n(H, m, r, r)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
(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)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ()]]