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Proof step 22 from proof add-preserves-reachable-rev (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
H[r1].nxt = H[ce.nxt].nxt, path(H[r].nxt ' + x, H[r1, ce]), reachable(r1, H[r].nxt, H), r1 ∈ H, ce.nxt ∈ H, r ∈ H, ∀ H, r1, ce, r. H[r1].nxt = H[ce.nxt].nxt ∧ path(r ' + x, H[r1, ce]) ∧ reachable(r1, H[r].nxt, H) ∧ ce.nxt ∈ H ∧ r1 ∈ H → (ce.nxt ' + x).last = ce.nxt ∨ ce.nxt = null ∨ r1 = null ∨ reachable(r1, (r ' + x).last, H) ∨ reachable(r1, ce.nxt, H) ⊦ (H[r].nxt ' + x).last = ce.nxt, ce.nxt = null, r = r1, r = null, r1 = null, reachable(r1, (H[r].nxt ' + x).last, H), reachable(r1, ce.nxt, H)

Rule argument

Additional information

Used simplifier rules: ⊦ r ≠ r0 → (r ∈ H[r0, ce] ↔ r ∈ H); (s)