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Proof step 12 from proof add-preserves-reachable-rev (previous step)

H[r1].nxt = H[ce.nxt].nxt, r = r1, 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], 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, 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 13:
H[r1].nxt = H[ce.nxt].nxt, path(ce.nxt ' + x0, H[r1, ce]), (ce.nxt ' + x0).last ∈ H[r1, ce], r1 ∈ H, ce.nxt ∈ H ⊦ (ce.nxt ' + x0).last = ce.nxt, ce.nxt = null, r1 = null, reachable(r1, ce.nxt, H), reachable(r1, (ce.nxt ' + x0).last, 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)