Theorems · Theorem · order theory
LowerSet.coe_subset_coe
∀ {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 61 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LE
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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 · cited by 8,199
- LowerSetstatement and proof · cited by 230
Cited by1
Results whose statement or proof uses this declaration.
- lowerClosure_leproof · cited by 3