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Proof step 9 from proof add-preserves-reachable-rev (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
H[r1].nxt = H[ce.nxt].nxt, path(H[r1, ce][r].nxt ' + x0, H[r1, ce]), reachable(r, r1, H), r ∈ H[r1, ce], (H[r1, ce][r].nxt ' + x0).last ∈ H[r1, ce], r1 ∈ H, ce.nxt ∈ H, reachable(H[r1, ce][r].nxt, r1, H) → reachable(H[r1, ce][r].nxt, (H[r1, ce][r].nxt ' + x0).last, H) ∨ reachable(H[r1, ce][r].nxt, ce.nxt, H) ⊦ (H[r1, ce][r].nxt ' + x0).last = ce.nxt, ce.nxt = null, r = null, reachable(r, (H[r1, ce][r].nxt ' + x0).last, H), reachable(r, ce.nxt, H)

Proof step 9 from proof add-preserves-reachable-rev (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information