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Proof step 10 from proof add-preserves-reachable (previous step)

r = r1, 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 = 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 11:
H[r1].nxt = H[ce.nxt].nxt, (H[r1].nxt ' + x0).last ∈ H, ce.nxt ∈ H, path(H[r1].nxt ' + x0, H), r1 ∈ H, reachable(H[r1].nxt, r1, H) → reachable(H[r1].nxt, (H[r1].nxt ' + x0).last, H[r1, ce]) ∨ reachable(H[r1].nxt, ce.nxt, H) ⊦ r1 = null, ce.nxt = null, reachable(r1, (H[r1].nxt ' + x0).last, H[r1, ce]), reachable(r1, ce.nxt, H)

Rule argument

Additional information

Used simplifier rules: self-reachable: ⊦ reachable(r, r, H) ↔ ¬ ¬(r ≠ null ∧ r ∈ H);