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Proof step 34 from proof add-preserves-reachable-rev (previous step)

x = [], 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], r ∈ H, H[r].nxt ∈ H, ce.nxt ∈ H ⊦ ce.nxt ' + H[H[r].nxt, ce][ce.nxt].nxt ' + x = [], r = null, (H[H[r].nxt, ce][ce.nxt].nxt ' + x).last = ce.nxt, H[r].nxt = null, ce.nxt = null, r = H[r].nxt, 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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 35:
H[H[r].nxt].nxt = H[ce.nxt].nxt, ce.nxt ∈ H[H[r].nxt, ce], r ∈ H, H[r].nxt ∈ H, ce.nxt ∈ H, H[H[r].nxt, ce][ce.nxt].nxt ∈ H[H[r].nxt, ce] ⊦ H[r].nxt = null, ce.nxt = null, r = H[r].nxt, ce.nxt ' + H[H[r].nxt, ce][ce.nxt].nxt ' = [], r = null, H[H[r].nxt, ce][ce.nxt].nxt = ce.nxt, H[H[r].nxt, ce][ce.nxt].nxt = null, reachable(H[r].nxt, ce.nxt, H), reachable(H[r].nxt, H[H[r].nxt, ce][ce.nxt].nxt, H), H[ce.nxt].nxt ≠ null ∧ H[ce.nxt].nxt ∈ H

Rule argument

Additional information

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