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Theorem path-split-last

⊦ path(r ' + x + r0 ', H) ↔ path(r ' + x, H) ∧ H[(r ' + x).last].nxt = r0 ∧ r0 ∈ H ∧ r0 ≠ null

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: acyclic-rem-not-reachable, linearity, reachable-addnew-rev, reachable-split-last, rem-stays-reachable-aux1, rem-stays-reachable-aux2,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 2
Proof steps: 4
Used lemmas: path-cons, path-one, path-two,
Used spec theorems:
- Used simplifier rules:
  - list/reflist/Nil
  - list/reflist/app
  - list-last/reflist/l
  - list-last/reflist/l-05
  - list/reflist/c
  - list/reflist/a