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Proof step 8 from proof acyclic-rem-not-reachable (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
ce.nxt = H[H[r0].nxt].nxt, reachable(H[r0].nxt, r0, H), H[r0].nxt ∈ H[r0, ce], r0 ∈ H, H[r0].nxt ∈ H, ∀ r1. ¬ reachable(H[r1].nxt, r1, H) ⊦ H[r0].nxt = null

Rule argument

Additional information

Used simplifier rules: path-one: ⊦ path(r ', H) ↔ r ∈ H ∧ r ≠ null;% ⊦ ¬ dups([]); (s)% ⊦ ¬ r ∈ []; (s)% ⊦ r '.last = r; (s)%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ x0 + [] = x0; (s)