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Proof step 14 from proof k-reachable-def (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
r ∈ H, H[r].nxt ∈ H ⊦ r = null, H[r].nxt = null, ∃ n. reachable-n(H, n, r, H[r].nxt)

Rule argument

Additional information

Used simplifier rules: path-one: ⊦ path(r ', H) ↔ ¬ ¬(r ∈ H ∧ r ≠ null);%l: ⊦ r '.last = r; from specification list-last[reflist]%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%app: ⊦ x0 + [] = x0; from specification list[reflist]