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Proof step 66 from proof acyclic-rem-not-reachable (previous step)

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

User applied rule all left

And obtained the following new goals

Proof step 67:
H[H[ce.nxt].nxt].nxt = ce.nxt, H[ce.nxt].nxt ∈ H, ce.nxt ∈ H, path(r ' + x1 + H[ce.nxt].nxt ', H), ¬ reachable(H[ce.nxt].nxt, ce.nxt, H) ⊦ ce.nxt = null, H[ce.nxt].nxt = null, r = H[ce.nxt].nxt, ce.nxt = r, ce.nxt = H[ce.nxt].nxt, dups(x1), ce.nxt ∈ x1, r ∈ x1, H[ce.nxt].nxt ∈ x1

Rule argument

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

Additional information

Used terms: ce.nxt