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Proof step 65 from proof rem-stays-reachable-aux (previous step)

x1 = r0 + x0, ce.nxt = H[H[r].nxt].nxt, path(H[r].nxt ' + x1 + H[r].nxt ', H), H[r].nxt ∈ H, r ∈ H ⊦ H[r].nxt = ce.nxt, H[r].nxt = null, r = null, r ∈ x1, ∃ x. path(r ' + x, H[r, ce]) ∧ (r ' + x).last = H[r].nxt

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 66:
ce.nxt = H[H[r].nxt].nxt, path(ce.nxt ' + x0 + H[r].nxt ', H), r ∈ H, H[r].nxt ∈ H ⊦ r = ce.nxt, r = null, H[r].nxt = null, H[r].nxt = ce.nxt, r ∈ x0, ∃ x. path(r ' + x, H[r, ce]) ∧ (r ' + x).last = H[r].nxt

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));%in-06: ⊦ ¬ r ∈ r0 ' + x0 ↔ r ≠ r0 ∧ ¬ r ∈ x0; from specification list[reflist]%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%c: ⊦ r + x0 = r ' + x0; from specification list[reflist]