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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: 9
Proof steps: 22
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:
  - map/insin
  - map/At-same
  - map/In-insert
  - list/a