Theorems · Theorem · order theory
UpperSet.coe_erase
∀ {α : Type u_1} [inst : Preorder α] (s : UpperSet α) (a : α), ↑(s.erase a) = ↑s \ ↑(LowerSet.Iic a)- Defined in
- Mathlib.Order.UpperLower.Closure
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses no axioms
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Preorderstatement and proof · cited by 7,952
- UpperSetstatement and proof · cited by 245
- LowerSetstatement · cited by 230
- LowerSet.Iicstatement · cited by 37
- UpperSet.erasestatement · cited by 9
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.