Theorems · Theorem · order theory
UpperSet.erase_eq
∀ {α : Type u_1} [inst : Preorder α] {s : UpperSet α} {a : α}, s.erase a = s ↔ a ∉ s- Defined in
- Mathlib.Order.UpperLower.Closure
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Preorder
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.
- Preorderstatement and proof · cited by 7,952
- UpperSetstatement and proof · cited by 245
- UpperSet.erasestatement · cited by 9
- UpperSet.sdiff_singletonproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- UpperSet.lt_eraseproof · cited by 1