Theorems · Theorem · order theory
isGLB_iff_le_iff
∀ {α : Type u_1} [inst : Preorder α] {s : Set α} {a : α}, IsGLB s a ↔ ∀ (b : α), b ≤ a ↔ b ∈ lowerBounds s- Defined in
- Mathlib.Order.Bounds.Basic
- Cited by
- 3 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 and proof · cited by 53,352
- Preorderstatement and proof · cited by 7,952
- le_rflproof · cited by 1,558
- IsGLBstatement and proof · cited by 213
- lowerBoundsstatement and proof · cited by 212
- le_isGLB_iffproof · cited by 17
Cited by3
Results whose statement or proof uses this declaration.
- isGLB_image2_of_isGLB_isGLBproof · cited by 5
- IsMinOn.isGLBproof · cited by 2
- MonotoneOn.sInf_image_Iccproof · cited by 1