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Proof step 33 from proof add-preserves-reachable-rev (previous step)

H[H[r].nxt].nxt = H[ce.nxt].nxt, x0 = r0 + x, path(ce.nxt ' + x0, H[H[r].nxt, ce]), H[r].nxt ∈ H, ce.nxt ∈ H, r ∈ H ⊦ ce.nxt ' + x0 = [], (ce.nxt ' + x0).last = ce.nxt, ce.nxt = null, H[r].nxt = null, r = H[r].nxt, r = null, reachable(H[r].nxt, (ce.nxt ' + x0).last, H), reachable(H[r].nxt, ce.nxt, H), H[ce.nxt].nxt ≠ null ∧ H[ce.nxt].nxt ∈ H

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 34:
H[H[r].nxt].nxt = H[ce.nxt].nxt, path(H[H[r].nxt, ce][ce.nxt].nxt ' + x, H[H[r].nxt, ce]), ce.nxt ∈ H[H[r].nxt, ce], H[r].nxt ∈ H, ce.nxt ∈ H, r ∈ H ⊦ ce.nxt ' + H[H[r].nxt, ce][ce.nxt].nxt ' + x = [], (H[H[r].nxt, ce][ce.nxt].nxt ' + x).last = ce.nxt, ce.nxt = null, H[r].nxt = null, r = H[r].nxt, r = null, reachable(H[r].nxt, (H[H[r].nxt, ce][ce.nxt].nxt ' + x).last, H), reachable(H[r].nxt, ce.nxt, H), H[ce.nxt].nxt ≠ null ∧ H[ce.nxt].nxt ∈ H

Rule argument

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 ' + x0).last = (r0 ' + x0).last; (s)%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ r + x0 = r ' + x0; (s)