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Proof step 62 from proof add-preserves-reachable-rev (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 63:
H[r1].nxt = H[ce.nxt].nxt, r1 ∈ H, path(H[r].nxt ' + x0, H[r1, ce]), r ∈ H, ce.nxt ∈ H, reachable(r, r1, H), reachable(H[r].nxt, ce.nxt, H), x0.last ∈ H[r1, ce] ⊦ ce.nxt = null, r = r1, x0 = [], r = null, x0.last = ce.nxt, 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]%l-02: ⊦ x0 ≠ [] → (r ' + x0).last = x0.last; from specification list-last[reflist]