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Proof step 12 from proof k-reachable-def (previous step)

∀ r, H. path(r ' + x0, H) → x0 = [] ∨ r = null ∨ (∃ n. reachable-n(H, n, r, x0.last)), path(r ' + (r0 + x0), H) ⊦ r0 + x0 = [], r = null, ∃ n. reachable-n(H, n, r, (r0 + x0).last)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
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)

Rule argument

Additional information

Used simplifier rules: path-cons: ⊦ path(r ' + r0 ' + x, H) ↔ ¬ ¬(r ∈ H ∧ r ≠ null ∧ H[r].nxt = r0 ∧ path(r0 ' + x, H));%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%e-01: ⊦ r ' + x0 ≠ []; from specification list[reflist]%c: ⊦ r + x0 = r ' + x0; from specification list[reflist]