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Proof step 56 from proof acyclic-rem-not-reachable (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 57:
ce.nxt = H[H[x.last].nxt].nxt, path(r ' + x, H), path(r ' + x1 + H[x.last].nxt ', H), x.last ∈ H, H[x.last].nxt ∈ H, ∀ r1. ¬ reachable(H[r1].nxt, r1, H) ⊦ x.last = r, x.last = H[x.last].nxt, H[x.last].nxt = null, r = H[x.last].nxt, x = [], dups(x1), dups(x), H[x.last].nxt ∈ x1, r ∈ x1, x.last ∈ x1, r ∈ x

Proof step 56 from proof acyclic-rem-not-reachable (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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