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Proof step 4 from proof acyclic-rem-not-reachable (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
ce.nxt = H[H[r0].nxt].nxt, (r ' + x).last = H[r0].nxt, path(r ' + x, H[r0, ce]), reachable(r, r0, H), H[r0].nxt ∈ H, H[r0].nxt ∈ H[r0, ce], r0 ∈ H, ∀ r1. ¬ reachable(H[r1].nxt, r1, H) ⊦ H[r0].nxt = null, r ∈ x, dups(x)

Rule argument

Additional information

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