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Proof step 7 from proof rem-reachable (previous step)

ce.nxt = H[H[r1].nxt].nxt, path(r ' + (r0 + x0), H), H[r1].nxt ∈ H, r1 ∈ H, ∀ ce, H, r1, r. ce.nxt = H[H[r1].nxt].nxt ∧ path(r ' + x0, H) ∧ r1 ∈ H ∧ H[r1].nxt ∈ H → (r ' + x0).last = H[r1].nxt ∨ H[r1].nxt = null ∨ r1 = null ∨ reachable(r, (r ' + x0).last, H[r1, ce]) ⊦ (r ' + (r0 + x0)).last = H[r1].nxt, H[r1].nxt = null, r1 = null, reachable(r, (r ' + (r0 + x0)).last, H[r1, ce])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
ce.nxt = H[H[r1].nxt].nxt, path(H[r].nxt ' + x0, H), r ∈ H, H[r1].nxt ∈ H, r1 ∈ H, ∀ ce, H, r1, r. ce.nxt = H[H[r1].nxt].nxt ∧ path(r ' + x0, H) ∧ r1 ∈ H ∧ H[r1].nxt ∈ H → (r ' + x0).last = H[r1].nxt ∨ H[r1].nxt = null ∨ r1 = null ∨ reachable(r, (r ' + x0).last, H[r1, ce]) ⊦ (H[r].nxt ' + x0).last = H[r1].nxt, H[r1].nxt = null, r = null, r1 = null, reachable(r, (H[r].nxt ' + x0).last, H[r1, ce])

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)