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Proof step 13 from proof reachable-split-last (previous step)

path(r ' + x1 + r0 ', H), r0 ∈ H ⊦ r = r0, reachable(r, (r ' + x1).last, H) ∧ H[(r ' + x1).last].nxt = r0 ∧ H[(r ' + x1).last].nxt ≠ null

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
path(r ' + x1 + r0 ', H), r0 ∈ H ⊦ r = r0, reachable(r, (r ' + x1).last, H) ∧ H[(r ' + x1).last].nxt ≠ null

Rule argument

Additional information

Used simplifier rules: path-last-nxt: ⊦ path(r ' + x + r0 ', H) → (H[(r ' + x).last].nxt ≠ r0 ↔ false);%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]