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Proof step 49 from proof add-preserves-reachable-rev (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 50:
H[r1].nxt = H[ce.nxt].nxt, path(H[r1, ce][ce.nxt].nxt ' + x, H[r1, ce]), ce.nxt ∈ H[r1, ce], r1 ∈ H, (H[r1, ce][ce.nxt].nxt ' + x).last ∈ H[r1, ce], ce.nxt ∈ H ⊦ (H[r1, ce][ce.nxt].nxt ' + x).last = ce.nxt, r1 = null, ce.nxt = null, reachable(r1, (H[r1, ce][ce.nxt].nxt ' + x).last, H), reachable(r1, ce.nxt, H), H[r1].nxt ∈ H ∧ H[r1].nxt ≠ null

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));%l-05: ⊦ (r ' + r0 ' + x0).last = (r0 ' + x0).last; from specification list-last[reflist]%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%c: ⊦ r + x0 = r ' + x0; from specification list[reflist]