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Proof step 17 from proof add-preserves-reachable-rev (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
H[r1].nxt = H[ce.nxt].nxt, path(H[r1, ce][r].nxt ' + x, H[r1, ce]), reachable(r1, H[r].nxt, H), r ∈ H[r1, ce], r1 ∈ H, ce.nxt ∈ H, ∀ H, r1, ce, r. H[r1].nxt = H[ce.nxt].nxt ∧ path(r ' + x, H[r1, ce]) ∧ reachable(r1, H[r].nxt, H) ∧ ce.nxt ∈ H ∧ r1 ∈ H → (ce.nxt ' + x).last = ce.nxt ∨ ce.nxt = null ∨ r1 = null ∨ reachable(r1, (r ' + x).last, H) ∨ reachable(r1, ce.nxt, H) ⊦ (H[r1, ce][r].nxt ' + x).last = ce.nxt, ce.nxt = null, r = null, r1 = null, reachable(r1, (H[r1, ce][r].nxt ' + x).last, H), reachable(r1, ce.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)