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Proof step 16 from proof k-reachable-def (previous step)

path(H[r].nxt ' + x0, H), r ∈ H, ∀ r, H. path(r ' + x0, H) → r = null ∨ x0 = [] ∨ (∃ n. reachable-n(H, n, r, x0.last)) ⊦ r = null, x0 = [], ∃ n. reachable-n(H, n, r, (H[r].nxt ' + x0).last)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
path(H[r].nxt ' + x0, H), r ∈ H, ∀ r0, H0. path(r0 ' + x0, H0) → r0 = null ∨ (∃ n. reachable-n(H0, n, r0, x0.last)) ⊦ r = null, x0 = [], ∃ n. reachable-n(H, n, r, x0.last)

Rule argument

Additional information

Used simplifier rules: a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ x0 ≠ [] → (x1 + x0).last = x0.last; (s)