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Proof step 43 from proof add-preserves-reachable (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 44:
H[r1].nxt = H[ce.nxt].nxt, reachable(H[r].nxt, r1, H), (H[r].nxt ' + x0).last ∈ H, reachable(r, r1, H), ce.nxt ∈ H, path(H[r].nxt ' + x0, H), r ∈ H, r1 ∈ H, reachable(H[r].nxt, (H[r].nxt ' + x0).last, H[r1, ce]) ∨ reachable(H[r].nxt, ce.nxt, H) ⊦ r = r1, r = null, ce.nxt = null, reachable(r, (H[r].nxt ' + x0).last, H[r1, ce]), reachable(r, ce.nxt, H)

Rule argument

Additional information

Used simplifier rules: fromnext-reachable: ⊦ reachable(r, r0, H) ∧ r ≠ r0 → (¬ reachable(H[r].nxt, r0, H) ↔ false);