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Proof step 7 from proof add-preserves-reachable (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
H[r1].nxt = H[ce.nxt].nxt, path(H[r].nxt ' + x0, H), reachable(r, r1, H), r ∈ H, ce.nxt ∈ H, ∀ H, r1, ce, r. H[r1].nxt = H[ce.nxt].nxt ∧ path(r ' + x0, H) ∧ reachable(r, r1, H) ∧ ce.nxt ∈ H → ce.nxt = null ∨ reachable(r, ce.nxt, H) ∨ reachable(r, (r ' + x0).last, H[r1, ce]) ⊦ ce.nxt = null, r = null, reachable(r, (H[r].nxt ' + x0).last, H[r1, ce]), reachable(r, 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)