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Proof step 80 from proof acyclic-rem-not-reachable (previous step)

ce.nxt = H[H[r0].nxt].nxt, path(r ' + x1 + H[r0].nxt ', H), path(r ' + x1 + H[r0].nxt ' + (ce.nxt ' + x2) + r0 ', H), path(ce.nxt ' + x2 + r0 ', H), r0 ∈ H, H[r0].nxt ∈ H, ∀ r1. ¬ reachable(H[r1].nxt, r1, H) ⊦ H[r0].nxt = null, H[r0].nxt = ce.nxt, r = H[r0].nxt, r = ce.nxt, r0 = r, r0 = H[r0].nxt, r0 = ce.nxt, dups(x1 + x2), dups(x1), dups(x2), H[r0].nxt ∈ x1, r ∈ x1, r0 ∈ x1, r ∈ x2, r0 ∈ x2, H[r0].nxt ∈ x2, ce.nxt ∈ x1, ce.nxt ∈ x2, path(ce.nxt ' + x2 + (r0 ' + H[r0].nxt), H) ∧ (ce.nxt ' + x2 + (r0 ' + H[r0].nxt)).last = H[r0].nxt

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 81:
ce.nxt = H[H[r0].nxt].nxt, path(ce.nxt ' + x2 + r0 ', H), path(r ' + x1 + H[r0].nxt ' + (ce.nxt ' + x2) + r0 ', H), path(r ' + x1 + H[r0].nxt ', H), H[r0].nxt ∈ H, r0 ∈ H, ∀ r1. ¬ reachable(H[r1].nxt, r1, H) ⊦ H[r0].nxt = ce.nxt, H[r0].nxt = null, r = ce.nxt, r = H[r0].nxt, r0 = ce.nxt, r0 = H[r0].nxt, r0 = r, dups(x2), dups(x1), dups(x1 + x2), path(ce.nxt ' + x2 + r0 ' + H[r0].nxt ', H), ce.nxt ∈ x2, ce.nxt ∈ x1, H[r0].nxt ∈ x2, r0 ∈ x2, r ∈ x2, r0 ∈ x1, r ∈ x1, H[r0].nxt ∈ x1

Rule argument

Additional information

Used simplifier rules: ⊦ (x0 + r ').last = r; (s)%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ x0 + r = x0 + r '; (s)