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Proof step 19 from proof reach-reachnext (previous step)

∀ r, H. (r ' + x).last = H[r].nxt ∧ path(r ' + x, H) ∧ r ∈ H ∧ (H[r].nxt = null ∨ ¬ H[r].nxt ∈ H) → r = null, (r ' + (r0 + x)).last = H[r].nxt, path(r ' + (r0 + x), H), r ∈ H, H[r].nxt = null ∨ ¬ H[r].nxt ∈ H ⊦ r = null

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 20:
(H[r].nxt ' + x).last = H[r].nxt, path(H[r].nxt ' + x, H), r ∈ H, H[r].nxt = null ∨ ¬ H[r].nxt ∈ H, ∀ r, H. (r ' + x).last = H[r].nxt ∧ path(r ' + x, H) ∧ r ∈ H ∧ (H[r].nxt = null ∨ ¬ H[r].nxt ∈ H) → r = null ⊦ r = null

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));%l-05: ⊦ (r ' + r0 ' + x0).last = (r0 ' + x0).last; from specification list-last[reflist]%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%c: ⊦ r + x0 = r ' + x0; from specification list[reflist]