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Theorem path-last

⊦ path(r ' + x, H) → (¬ (r ' + x).last ∈ H ↔ false)

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by: add-preserves-reachable, changenonnxt-reachable, modified-stays-reachable, modnotreachable-reachable, modnotreachable-reachable-rev, path-prelast, reach-alloc, reach-reachnext, reachable-addnew-rev, reachable-addnewtonull-rev, reachable-modbehind, reachable-trans, rem-reachable, rem-reachable-rev-weak,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 1
Proof steps: 8
Used lemmas: path-cons, path-one,
Used spec theorems:
- Used simplifier rules:
  - list/reflist/app
  - list-last/reflist/l
  - list-last/reflist/l-02
  - list/reflist/a
  - list/reflist/e-01
  - list/reflist/c