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Proof step 4 from proof reach-n-path-n (previous step)

n0 = 0, n0 ≠ 0 → (∀ H, r, r0. reachable-n(H, n0, r, r0) ↔ (∃ x. path(x, H) ∧ hd x = r ∧ x.last = r0 ∧ # x = n0 + 1)) ⊦ (∃ r1. reachable-1(H, r, r1) ∧ reachable-n(H, n0, r1, r0)) ↔ (∃ x. path(x, H) ∧ hd x = r ∧ x.last = r0 ∧ # x = 2 + n0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: reachable-n-base: ⊦ reachable-n(H, 0, r, r0) ↔ r = r0;