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Theorem ole-in

⊦ ordered≤(a ' + x) ∧ b ∈ x → ¬ b < a

Type: A user defined theorem
Validity: The proof is valid.
Features: forward, localforward,
Comment:
Used by: ole-last, orderedle-ls,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 1
Proof steps: 4
Used lemmas: le-r, app-01, cons-02,
Used spec theorems:
- Used simplifier rules:
  - list/in-empty
  - list/a
  - list/in-rec
  - list/c
  - oelem/nll
  - oelem/nnn