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Proof step 57 from proof add-preserves-reachable (previous step)

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

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);% ⊦ r ≠ r0 → H[r0, ce][r] = H[r]; (s)%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ (r ' + r0 ' + x0).last = (r0 ' + x0).last; (s)% ⊦ r ∈ H[r0, ce] ↔ r = r0 ∨ r ∈ H; (ws) Used terms: H[r].nxt ' + x