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Theorem ole-01

⊦ ordered≤(ins≤(a, x)) ↔ ordered≤(x)

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by: ole,
Used by units in proved state: olist-sort,
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 4
Proof steps: 15
Used lemmas: app-01, cons-02, le-r, ins-y, empty, ole-rec, ins-n, le-e, le-o, ins-e,
Used spec theorems:
- Used simplifier rules:
  - list/c-08
  - list-data/elim-list-c
  - list/c-07
  - list/c-03
  - list/app
  - list/in-17
  - list/e-01
  - list/in-14
  - oelem/nen
  - list/in-rec
  - oelem/transitivity
  - oelem/irreflexivity
  - oelem/nll
  - oelem/lel
  - list/c-06
  - list/a
  - list/c