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Proof step 41 from proof add-preserves-reachable-rev (previous step)

H[r1].nxt = H[ce.nxt].nxt, path(H[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[H[r].nxt].nxt ' + x0 = [], (H[H[r].nxt].nxt ' + x0).last = ce.nxt, ce.nxt = null, H[r].nxt = null, H[r].nxt = r1, r = r1, r = null, r1 = null, reachable(r1, ce.nxt, H), reachable(r1, (H[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 42:
H[r1].nxt = H[ce.nxt].nxt, path(H[H[r].nxt].nxt ' + x0, H[r1, ce]), reachable(r1, H[r].nxt, H), r ∈ H, ce.nxt ∈ H, r1 ∈ H, H[r].nxt ∈ H ⊦ H[H[r].nxt].nxt ' + x0 = [], (H[H[r].nxt].nxt ' + x0).last = ce.nxt, H[r].nxt = r1, H[r].nxt = null, ce.nxt = null, r = null, r = r1, r1 = null, reachable(r1, (H[H[r].nxt].nxt ' + x0).last, H), reachable(r1, ce.nxt, H), H[H[r].nxt].nxt ≠ null ∧ H[H[r].nxt].nxt ∈ H

Rule argument

Additional information

Used simplifier rules: ⊦ r ∈ H[r0, ce] ↔ r = r0 ∨ r ∈ H; (ws)