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Proof step 19 from proof acyclic-rem-not-reachable (previous step)

ce.nxt = H[ce.nxt].nxt, ce.nxt = H[r0].nxt, reachable(r, r0, H), ce.nxt ∈ H, r0 ∈ H, path(r ' + x0 + r0 ' + ce.nxt ', H[r0, ce]), ∀ r1. ¬ reachable(H[r1].nxt, r1, H) ⊦ ce.nxt = null, r = ce.nxt, r = r0, ce.nxt = r0, r0 = null, r ∈ x0, ce.nxt ∈ x0, r0 ∈ x0, dups(x0)

User applied rule all left

And closed the goal!

Rule argument

pos: left 7 terms: ce.nxt abort: F discard: T computed: F

Additional information

Used simplifier rules: self-reachable: ⊦ reachable(r, r, H) ↔ ¬ ¬(r ≠ null ∧ r ∈ H); Used terms: ce.nxt