Theorems · Theorem · order theory
isLUB_congr
∀ {α : Type u_1} [inst : Preorder α] {s t : Set α} {a : α}, upperBounds s = upperBounds t → (IsLUB s a ↔ IsLUB t a)- Defined in
- Mathlib.Order.Bounds.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- IsLUBstatement and proof · cited by 280
- upperBoundsstatement and proof · cited by 263
- IsLeastproof · cited by 122
Cited by4
Results whose statement or proof uses this declaration.
- isLUB_iff_of_subset_of_subset_closureproof · cited by 2
- Dense.ciSupproof · cited by 2
- ScottContinuousOn.fromProdproof · cited by 1
- isLUB_iUnion_iff_of_isLUBproof · cited by 1