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Proof step 22 from proof removed-stays-reachable (previous step)

ce.nxt = H[H[r0].nxt].nxt, (∃ r1. reachable(r, r1, H) ∧ H[r0].nxt = H[r1].nxt ∧ ¬ reachable(r0, r1, H)) ↔ (∃ x. path(r ' + x + H[r0].nxt ', H) ∧ r0 ≠ r ∧ ¬ r0 ∈ x), reachable(ce.nxt, H[r0].nxt, H) ∧ ¬ reachable(ce.nxt, r0, H) ↔ (∃ x. path(H[r0].nxt ' + x + H[r0].nxt ', H) ∧ ¬ r0 ∈ x), reachable(r, r0, H), r0 ∈ H, H[r0].nxt ∈ H, H[r0].nxt = r0 ∨ r ≠ H[r0].nxt, reachable(ce.nxt, H[r0].nxt, H) ∧ ¬ reachable(ce.nxt, r0, H) ∨ (∃ r1. reachable(r, r1, H) ∧ H[r1].nxt = H[r0].nxt ∧ ¬ reachable(r0, r1, H)) ⊦ H[r0].nxt = ce.nxt, H[r0].nxt = null, ∃ x. path(r ' + x + H[r0].nxt ', H) ∧ r0 ≠ r ∧ ¬ r0 ∈ x, ∃ x. path(H[r0].nxt ' + x + H[r0].nxt ', H) ∧ ¬ r0 ∈ x

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
ce.nxt = H[H[r0].nxt].nxt, H[r1].nxt = H[r0].nxt, reachable(r, r0, H), reachable(r, r1, H), H[r0].nxt ∈ H, r0 ∈ H, r1 ∈ H, H[r0].nxt = r0 ∨ r ≠ H[r0].nxt ⊦ H[r0].nxt = null, H[r0].nxt = ce.nxt, reachable(r0, r1, H), ∃ x. path(H[r0].nxt ' + x + H[r0].nxt ', H) ∧ ¬ r0 ∈ x, ∃ r1. reachable(r, r1, H) ∧ H[r0].nxt = H[r1].nxt ∧ ¬ reachable(r0, r1, H), ∃ x. path(r ' + x + H[r0].nxt ', H) ∧ ¬ r0 ∈ x, reachable(ce.nxt, H[r0].nxt, H) ∧ ¬ reachable(ce.nxt, r0, H)

Rule argument

Additional information

Used simplifier rules: reach-alloc: ⊦ reachable(r, r1, H) → r1 ∈ H;