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Proof step 13 from proof reach-reachnext (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
(H[r].nxt ' + x0).last ∈ H, path(H[r].nxt ' + x0, H), r ∈ H, H[(H[r].nxt ' + x0).last].nxt ∈ H, ∀ H0, r1. H0[(r1 ' + x0).last].nxt ∈ H0 ∧ path(r1 ' + x0, H0) → H0[(r1 ' + x0).last].nxt = null ∨ path(r1 ' + x0 + H0[(r1 ' + x0).last].nxt ', H0) ⊦ r = null, H[(H[r].nxt ' + x0).last].nxt = null, path(H[r].nxt ' + x0 + H[(H[r].nxt ' + x0).last].nxt ', 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-last: ⊦ path(r ' + x, H) → (¬ (r ' + x).last ∈ H ↔ false);%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]