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Proof step 65 from proof add-preserves-reachable-rev (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 66:
H[r1].nxt = H[ce.nxt].nxt, path(H[r].nxt ' + x0, H[r1, ce]), reachable(H[r].nxt, ce.nxt, H), reachable(r, r1, H), r ∈ H, ce.nxt ∈ H, r1 ∈ H, x0.last ∈ H[r1, ce] ⊦ x0.last = ce.nxt, ce.nxt = null, r = r1, r = null, x0 = [], reachable(r, ce.nxt, H), reachable(r, x0.last, H)

Rule argument

Additional information

Used simplifier rules: a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ x0 ≠ [] → (r ' + x0).last = x0.last; (s)