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Proof step 16 from proof add-preserves-reachable-rev (previous step)

∀ H, r1, ce, r. H[r1].nxt = H[ce.nxt].nxt ∧ reachable(r1, H[r].nxt, H) ∧ path(r ' + x, H[r1, ce]) ∧ ce.nxt ∈ H ∧ r1 ∈ H → ce.nxt = null ∨ r1 = null ∨ (ce.nxt ' + x).last = ce.nxt ∨ reachable(r1, ce.nxt, H) ∨ reachable(r1, (r ' + x).last, H), H[r1].nxt = H[ce.nxt].nxt, reachable(r1, H[r].nxt, H), path(r ' + (r0 + x), H[r1, ce]), ce.nxt ∈ H, r1 ∈ H ⊦ ce.nxt = null, r1 = null, (ce.nxt ' + (r0 + x)).last = ce.nxt, 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 17:
H[r1].nxt = H[ce.nxt].nxt, path(H[r1, ce][r].nxt ' + x, H[r1, ce]), r ∈ 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 ∧ reachable(r1, H[r].nxt, H) ∧ path(r ' + x, H[r1, ce]) ∧ ce.nxt ∈ H ∧ r1 ∈ H → ce.nxt = null ∨ r1 = null ∨ (ce.nxt ' + x).last = ce.nxt ∨ reachable(r1, ce.nxt, H) ∨ reachable(r1, (r ' + x).last, H) ⊦ r = null, (H[r1, ce][r].nxt ' + x).last = ce.nxt, r1 = null, ce.nxt = 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));%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]