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Proof step 66 from proof acyclic-rem-not-reachable (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 67:
H[H[ce.nxt].nxt].nxt = ce.nxt, path(r ' + x1 + H[ce.nxt].nxt ', H), H[ce.nxt].nxt ∈ H, ce.nxt ∈ H, ∀ r1. ¬ reachable(H[r1].nxt, r1, H) ⊦ H[ce.nxt].nxt = null, ce.nxt = r, ce.nxt = H[ce.nxt].nxt, ce.nxt = null, r = H[ce.nxt].nxt, dups(x1), H[ce.nxt].nxt ∈ x1, r ∈ x1, ce.nxt ∈ x1

Rule argument

Additional information

Used simplifier rules: a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ (r ' + x0 + r0 ').last = r0; (s)