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Proof step 68 from proof rem-stays-reachable-aux (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 69:
ce.nxt = H[H[r].nxt].nxt, path(ce.nxt ' + x0 + H[r].nxt ', H), H[r].nxt ∈ H, r ∈ H ⊦ H[r].nxt = ce.nxt, H[r].nxt = null, r = ce.nxt, r = null, path(ce.nxt ' + x0 + H[r].nxt ', H[r, ce]), r ∈ x0

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 ' + x0 + r0 ').last = r0; (s)% ⊦ (r ' + r0 ' + x0).last = (r0 ' + x0).last; (s)%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ H[r, ce][r] = ce; (s)% ⊦ r ∈ H[r, ce]; (s)