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Proof step 42 from proof add-preserves-reachable-rev (previous step)

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

User applied rule constructor cut

And closed the goal!

Rule argument

var: x0

Additional information

Used simplifier rules: path-one: ⊦ path(r ', H) ↔ r ∈ H ∧ r ≠ null;%reach-reachnext: ⊦ reachable(r, r1, H) → ( reachable(r, H[r1].nxt, H) ↔ ¬(H[r1].nxt = null ∨ ¬ H[r1].nxt ∈ H));%path-cons: ⊦ path(r ' + r0 ' + x, H) ↔ r ∈ H ∧ r ≠ null ∧ H[r].nxt = r0 ∧ path(r0 ' + x, H);%reflist freely generated by [], +;;% ⊦ r + x0 = r ' + x0; (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)% ⊦ r = r0 → H[r0, ce][r] = ce; (s)% ⊦ x0 + [] = x0; (s)% ⊦ r '.last = r; (s)