Theorems · Theorem · order theory
lowerBounds_singleton
∀ {α : Type u_1} [inst : Preorder α] {a : α}, lowerBounds {a} = Set.Iic a- Defined in
- Mathlib.Order.Bounds.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses propext, Quot.sound
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Preorderstatement and proof · cited by 7,952
- Set.Iicstatement · cited by 1,111
- lowerBoundsstatement · cited by 212
- IsGLB.lowerBounds_eqproof · cited by 11
- isGLB_singletonproof · cited by 7
Cited by7
Results whose statement or proof uses this declaration.
- lowerBounds_insertproof · cited by 3
- DedekindCut.ofAttribute_eq_principalproof · cited by 1
- isGLB_iUnion_iff_of_isGLBproof · cited by 0
- RightOrdContinuous.monoproof · cited by 0
- eVariationOn.union'proof · cited by 0
- eVariationOn.image_range_of_monotoneproof · cited by 0
- isGLB_iUnion_iff_of_isLUBproof · cited by 0