Theorems · Theorem · order theory
IsGLB.lowerBounds_eq
∀ {α : Type u_1} [inst : Preorder α] {s : Set α} {a : α}, IsGLB s a → lowerBounds s = Set.Iic a- Defined in
- Mathlib.Order.Bounds.Basic
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses propext, Quot.sound
- 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 and proof · cited by 53,352
- Preorderstatement and proof · cited by 7,952
- Set.extproof · cited by 2,266
- Set.Iicstatement and proof · cited by 1,111
- IsGLBstatement and proof · cited by 213
- lowerBoundsstatement and proof · cited by 212
- lowerBounds_mono_memproof · cited by 3
Cited by11
Results whose statement or proof uses this declaration.
- le_isGLB_iffproof · cited by 17
- lowerBounds_singletonproof · cited by 7
- IsLeast.lowerBounds_eqproof · cited by 1
- lowerBounds_Iocproof · cited by 0
- lowerBounds_Icoproof · cited by 0
- lowerBounds_Iccproof · cited by 0
- lowerBounds_Iciproof · cited by 0
- isGLB_iUnion_iff_of_isGLBproof · cited by 0
- isGLB_iUnion_iff_of_isLUBproof · cited by 0
- lowerBounds_Ioiproof · cited by 0
- lowerBounds_Iooproof · cited by 0