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Proof step 20 from proof removed-stays-reachable (previous step)

ce.nxt = H[H[r0].nxt].nxt, path(r ' + x + H[r0].nxt ', H), reachable(r, r0, H), r0 ∈ H, H[r0].nxt ∈ H, ∃ x0. path(r ' + x0 + H[r0].nxt ', H) ∧ ¬ r0 ∈ x0, ∃ r1. reachable(r, r1, H) ∧ H[r0].nxt = H[r1].nxt ∧ ¬ reachable(r0, r1, H) ⊦ H[r0].nxt = ce.nxt, H[r0].nxt = null, r = H[r0].nxt, r0 = r, r0 ∈ x, ∃ x. path(H[r0].nxt ' + x + H[r0].nxt ', H) ∧ ¬ r0 ∈ x, ∃ r1. reachable(r, r1, H) ∧ H[r1].nxt = H[r0].nxt ∧ ¬ reachable(r0, r1, H), reachable(ce.nxt, H[r0].nxt, H) ∧ ¬ reachable(ce.nxt, r0, H)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
H[r0].nxt = H[r1].nxt, ce.nxt = H[H[r1].nxt].nxt, path(r ' + x0 + H[r1].nxt ', H), path(r ' + x + H[r1].nxt ', H), reachable(r, r1, H), reachable(r, r0, H), H[r1].nxt ∈ H, r0 ∈ H, r1 ∈ H ⊦ H[r1].nxt = null, H[r1].nxt = ce.nxt, r = H[r1].nxt, reachable(r0, r1, H), r0 ∈ x, r0 ∈ x0, ∃ r1. reachable(r, r1, H) ∧ H[r1].nxt = H[r0].nxt ∧ ¬ reachable(r0, r1, H), ∃ x. path(H[r1].nxt ' + x + H[r1].nxt ', H) ∧ ¬ r0 ∈ x, reachable(ce.nxt, H[r1].nxt, H) ∧ ¬ reachable(ce.nxt, r0, H)

Rule argument

Additional information

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