Theorems · Theorem · order theory
IsLeast.lowerBounds_eq
∀ {α : Type u_1} [inst : Preorder α] {s : Set α} {a : α}, IsLeast s a → lowerBounds s = Set.Iic a- Defined in
- Mathlib.Order.Bounds.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 8 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.Iicstatement · cited by 1,111
- lowerBoundsstatement · cited by 212
- IsLeaststatement and proof · cited by 122
- IsLeast.isGLBproof · cited by 23
- IsGLB.lowerBounds_eqproof · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- OrderBot.lowerBounds_univproof · cited by 0