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Proof step 31 from proof add-preserves-reachable-rev (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 32:
H[H[r].nxt].nxt = H[ce.nxt].nxt, path(ce.nxt ' + x0, H[H[r].nxt, ce]), r ∈ H, ce.nxt ∈ H, H[r].nxt ∈ H ⊦ ce.nxt ' + x0 = [], (ce.nxt ' + x0).last = ce.nxt, H[r].nxt = null, ce.nxt = null, r = null, r = H[r].nxt, reachable(H[r].nxt, ce.nxt, H), reachable(H[r].nxt, (ce.nxt ' + x0).last, H), H[ce.nxt].nxt ≠ null ∧ H[ce.nxt].nxt ∈ H

Rule argument

Additional information

Used simplifier rules: self-reachable: ⊦ reachable(r, r, H) ↔ r ≠ null ∧ r ∈ H;% ⊦ r ∈ H[r, ce]; (s)% ⊦ H[r, ce][r] = ce; (s)