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Proof step 27 from proof add-preserves-reachable-rev (previous step)

x = r0 + x0, H[r1].nxt = H[ce.nxt].nxt, reachable(r1, H[r].nxt, H), r1 ∈ H, ce.nxt ∈ H, path(H[r].nxt ' + x, H[r1, ce]), r ∈ H ⊦ r1 = null, ce.nxt = null, r = r1, x = [], r = null, x.last = ce.nxt, reachable(r1, ce.nxt, H), reachable(r1, x.last, H), H[H[r].nxt].nxt ≠ null ∧ H[H[r].nxt].nxt ∈ H

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 28:
H[r1].nxt = H[ce.nxt].nxt, path(H[r1, ce][H[r].nxt].nxt ' + x0, H[r1, ce]), H[r].nxt ∈ H[r1, ce], ce.nxt ∈ H, r1 ∈ H, reachable(r1, H[r].nxt, H), r ∈ H ⊦ H[r].nxt = null, (H[r1, ce][H[r].nxt].nxt ' + x0).last = ce.nxt, r = null, H[r1, ce][H[r].nxt].nxt ' + x0 = [], r = r1, ce.nxt = null, r1 = null, reachable(r1, (H[r1, ce][H[r].nxt].nxt ' + x0).last, H), reachable(r1, ce.nxt, H), H[H[r].nxt].nxt ≠ null ∧ H[H[r].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));%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%c: ⊦ r + x0 = r ' + x0; from specification list[reflist]