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Proof step 50 from proof acyclic-rem-not-reachable (previous step)

ce.nxt = H[H[r0].nxt].nxt, path(r ' + x1 + H[r0].nxt ', H), 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, r = H[r0].nxt, dups(x1), r0 ∈ x1, r ∈ x1, H[r0].nxt ∈ x1, r0 ∈ r ' + x1 + H[r0].nxt '

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 51:
ce.nxt = H[H[r0].nxt].nxt, path(r ' + x1 + H[r0].nxt ', H), reachable(r, r0, H), r0 ∈ H, H[r0].nxt ∈ H, ∀ r1. ¬ reachable(H[r1].nxt, r1, H) ⊦ H[r0].nxt = null, r = H[r0].nxt, r0 = r, r0 = H[r0].nxt, dups(x1), H[r0].nxt ∈ x1, r ∈ x1, r0 ∈ x1

Rule argument

Additional information

Used simplifier rules: ⊦ r ≠ r0 → (r ∈ H[r0, ce] ↔ r ∈ H); (s)%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ r ∈ r0 ' ↔ r = r0; (s)% ⊦ r ∈ x0 + x1 ↔ r ∈ x0 ∨ r ∈ x1; (s)% ⊦ r ∈ r0 ' + x0 ↔ ¬(r ≠ r0 ∧ ¬ r ∈ x0); (ss)