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Proof step 71 from proof acyclic-rem-not-reachable (previous step)

H[H[ce.nxt].nxt].nxt = ce.nxt, path(r ' + x1 + H[ce.nxt].nxt ', H), ce.nxt ∈ H, H[ce.nxt].nxt ∈ H ⊦ ce.nxt = null, ce.nxt = H[ce.nxt].nxt, ce.nxt = r, H[ce.nxt].nxt = null, r = H[ce.nxt].nxt, dups(x1), ce.nxt ∈ x1, r ∈ x1, H[ce.nxt].nxt ∈ x1, ∃ x. path(H[ce.nxt].nxt ' + x, H) ∧ (H[ce.nxt].nxt ' + x).last = ce.nxt

User applied rule exists right

And closed the goal!

Rule argument

pos: right 10 terms: ce.nxt ' abort: F discard: T computed: F

Additional information

Used simplifier rules: path-two: ⊦ path(r ' + r0 ', H) ↔ r ∈ H ∧ r0 ∈ H ∧ r ≠ null ∧ r0 ≠ null ∧ H[r].nxt = r0;%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ (x0 + r ').last = r; (s) Used terms: ce.nxt '