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Proof step 1 from proof rem-stays-reachable-aux (conclusion)

reachable(r, r0, H), H[r0].nxt ≠ null, H[r0].nxt ∈ H, H[r0].nxt ≠ H[H[r0].nxt].nxt, ce.nxt = H[H[r0].nxt].nxt ⊦ reachable(r, H[r0].nxt, H[r0, ce]) ↔ H[H[r0].nxt].nxt = H[r0].nxt ∨ r ≠ r0 ∧ r = H[r0].nxt ∨ (∃ 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 2:
ce.nxt = H[H[r0].nxt].nxt, reachable(r, r0, H), H[r0].nxt ∈ H, r0 ∈ H ⊦ H[r0].nxt = ce.nxt, H[r0].nxt = null, reachable(r, H[r0].nxt, H[r0, ce]) ↔ H[r0].nxt ≠ r0 ∧ r = H[r0].nxt ∨ (∃ x. path(r ' + x + H[r0].nxt ', H) ∧ r0 ≠ r ∧ ¬ r0 ∈ x) ∨ (∃ x. path(H[r0].nxt ' + x + H[r0].nxt ', H) ∧ ¬ r0 ∈ x)

Rule argument

Additional information

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