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Proof step 5 from proof acyclic-rem-not-reachable (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
(r ' + x).last = H[r0].nxt, ce.nxt = H[H[r0].nxt].nxt, path(r ' + x, H[r0, ce]), reachable(r, r0, H), H[r0].nxt ∈ H, r0 ∈ H, H[r0].nxt ∈ H[r0, ce], ∀ r1. ¬ reachable(H[r1].nxt, r1, H) ⊦ H[r0].nxt = null, dups(x), r ∈ x

Rule argument

Additional information

Used simplifier rules: a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ dups(r ' + x0) ↔ dups(x0) ∨ r ∈ x0; (ws)