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Proof step 9 from proof null-not-reachable (previous step)

(r0 + x0).last = null, path(r ' + (r0 + x0), H), ∀ r, H. x0.last = null ∧ path(r ' + x0, H) → x0 = [] ⊦ r0 + x0 = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
x0.last = null, path(H[r].nxt ' + x0, H), r ∈ H ⊦ r = null, x0 = [], ∃ r, H. path(r ' + x0, H)

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