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Proof step 52 from proof reachable-addnew-rev (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 53:
path(ce.nxt ' + x, H[H[r].nxt, ce]), (ce.nxt ' + x).last ∈ H, r ∈ H ⊦ H[r].nxt = ce.nxt, H[r].nxt = null, r = ce.nxt, r = null, r = H[r].nxt, dups(x), reachable(ce.nxt, (ce.nxt ' + x).last, H), reachable(r, (ce.nxt ' + x).last, H), ce.nxt ∈ x, H[r].nxt ∈ x, r ∈ x, H[r].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);% ⊦ dups(r ' + x0) ↔ dups(x0) ∨ r ∈ x0; (ws)% ⊦ r ∈ r0 ' + x0 ↔ ¬(r ≠ r0 ∧ ¬ r ∈ x0); (ss)% ⊦ H[r, ce][r] = ce; (s)% ⊦ r ∈ H[r0, ce] ↔ r = r0 ∨ r ∈ H; (ws)% ⊦ (r ' + r0 ' + x0).last = (r0 ' + x0).last; (s)%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ r + x0 = r ' + x0; (s)