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Proof step 34 from proof acyclic-rem-not-reachable (previous step)

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

User applied rule all left

And closed the goal!

Rule argument

pos: left 5 terms: ce.nxt abort: F discard: T computed: F

Additional information

Used simplifier rules: self-reachable: ⊦ reachable(r, r, H) ↔ ¬ ¬(r ≠ null ∧ r ∈ H);%reachable-notnullinH: ⊦ reachable(r, r1, H) → (¬ r1 ∈ H ↔ false); Used terms: ce.nxt