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Proof step 56 from proof add-preserves-reachable (previous step)

(H[r].nxt ' + x).last = ce.nxt, H[r1].nxt = H[ce.nxt].nxt, path(H[r].nxt ' + x, H), reachable(H[r].nxt, r1, H), (H[r].nxt ' + x0).last ∈ H, reachable(r, r1, H), ce.nxt ∈ H, path(H[r].nxt ' + x0, H), r ∈ H, r1 ∈ H ⊦ r = r1, r = null, ce.nxt = null, reachable(r, (H[r].nxt ' + x0).last, H[r1, ce]), ∃ x. path(r ' + x, H) ∧ (r ' + x).last = ce.nxt

User applied rule exists right

And closed the goal!

Rule argument

pos: right 5 terms: H[r].nxt ' + x abort: F discard: T computed: F

Additional information

Used simplifier rules: path-cons: ⊦ path(r ' + r0 ' + x, H) ↔ ¬ ¬(r ∈ H ∧ r ≠ null ∧ H[r].nxt = r0 ∧ path(r0 ' + x, H));%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%l-05: ⊦ (r ' + r0 ' + x0).last = (r0 ' + x0).last; from specification list-last[reflist] Used terms: H[r].nxt ' + x