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Theorem removed-stays-reachable

⊦ reachable(r, r0, H) ∧ H[r0].nxt ≠ null ∧ H[r0].nxt ∈ H ∧ 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 ∨ reachable(H[H[r0].nxt].nxt, H[r0].nxt, H) ∧ ¬ reachable(H[H[r0].nxt].nxt, r0, H) ∨ (∃ r1. reachable(r, r1, H) ∧ H[r1].nxt = H[r0].nxt ∧ ¬ reachable(r0, r1, H)))

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 8
Proof steps: 18
Used lemmas: rem-stays-reachable-aux2, rem-stays-reachable-aux1, endnotinH-notreachable, changenonnxt-reachable, reach-reachnext, rem-stays-reachable-aux, reach-alloc,
Used spec theorems:
- Used simplifier rules:
  - store/linheap/insin
  - store/linheap/At-same
  - store/linheap/In-insert
  - list/reflist/a