Theorems · Theorem · order theory
LowerSet.ext_iff
∀ {α : Type u_1} [inst : LE α] {s t : LowerSet α}, s = t ↔ ↑s = ↑t- Defined in
- Mathlib.Order.UpperLower.CompleteLattice
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
- Assumes
- LE
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- SetLike.coestatement and proof · cited by 8,199
- LowerSetstatement and proof · cited by 230
- LowerSet.extproof · cited by 29
Cited by1
Results whose statement or proof uses this declaration.
- LowerSet.Iio_eq_botproof · cited by 0