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Proof step 12 from proof reach-reachnext (previous step)

(r ' + x0).last = H[(r ' + []).last].nxt, path(r ' + [], H), path(r ' + x0, H), (r ' + []).last ∈ H ⊦ (r ' + x0).last ≠ null ∧ (r ' + x0).last ∈ H

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
(r ' + x0).last = H[r].nxt, path(r ' + x0, H), r ∈ H ⊦ r = null, H[r].nxt ≠ null ∧ H[r].nxt ∈ H

Rule argument

Additional information

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