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Proof step 24 from proof reach-reachnext (previous step)

path(r ' + (r0 + x0), H), (r ' + (r0 + x0)).last ∈ H, H[(r ' + (r0 + x0)).last].nxt ∈ H, ∀ r, H. path(r ' + x0, H) ∧ H[(r ' + x0).last].nxt ∈ 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 = 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 25:
path(H[r].nxt ' + x0, H), r ∈ H, (H[r].nxt ' + x0).last ∈ H, H[(H[r].nxt ' + x0).last].nxt ∈ H, ∀ r, H. path(r ' + x0, H) ∧ H[(r ' + x0).last].nxt ∈ H ∧ (r ' + x0).last ∈ H → H[(r ' + x0).last].nxt = null ∨ path(r ' + x0 + H[(r ' + x0).last].nxt ', H) ⊦ H[(H[r].nxt ' + x0).last].nxt = null, r = 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);% ⊦ (r ' + r0 ' + x0).last = (r0 ' + x0).last; (s)%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ r + x0 = r ' + x0; (s)