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Theorem self-reachable

⊦ reachable(r, r, H) ↔ ¬ ¬(r ≠ null ∧ r ∈ H)

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by: acyclic-rem-not-reachable, add-preserves-reachable, add-preserves-reachable-rev, frommodified, id-reachable, modnotreachable-reachable, modnotreachable-reachable-rev, modnotreachable-reachable-rev-weak, reachable-addnew, reachable-trans, rem-reachable, rem-reachable-rev-weak, rem-stays-reachable-aux1,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 4
Proof steps: 7
Used lemmas: path-cons, path-one, reachable-def,
Used spec theorems:
- Used simplifier rules:
  - list/reflist/c
  - list-last/reflist/l-05
  - list/reflist/app
  - list/reflist/a
  - list-last/reflist/l