Theorems · Theorem · order theory
IsLUB.upperBounds_eq
∀ {α : Type u_1} [inst : Preorder α] {s : Set α} {a : α}, IsLUB s a → upperBounds s = Set.Ici a- Defined in
- Mathlib.Order.Bounds.Basic
- Cited by
- 10 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.Icistatement and proof · cited by 1,070
- IsLUBstatement and proof · cited by 280
- upperBoundsstatement and proof · cited by 263
- upperBounds_mono_memproof · cited by 4
Cited by10
Results whose statement or proof uses this declaration.
- isLUB_le_iffproof · cited by 24
- upperBounds_singletonproof · cited by 4
- IsGreatest.upperBounds_eqproof · cited by 1
- isLUB_iUnion_iff_of_isLUBproof · cited by 1
- upperBounds_Iccproof · cited by 0
- upperBounds_Icoproof · cited by 0
- upperBounds_Iicproof · cited by 0
- upperBounds_Iioproof · cited by 0
- upperBounds_Iocproof · cited by 0
- upperBounds_Iooproof · cited by 0