Theorems · Theorem · order theory
isLeast_Icc
∀ {α : Type u_1} [inst : Preorder α] {a b : α}, b ≤ a → IsLeast (Set.Icc b a) b- Defined in
- Mathlib.Order.Bounds.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext, Quot.sound
- 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.
- Preorderstatement and proof · cited by 7,952
- Set.Iccstatement · cited by 1,702
- lowerBoundsproof · cited by 212
- IsLeaststatement and proof · cited by 122
- Set.left_mem_Iccproof · cited by 67
Cited by4
Results whose statement or proof uses this declaration.
- isGLB_Iccproof · cited by 2
- csInf_Iccproof · cited by 2
- HasConstantSpeedOnWith.Icc_Iccproof · cited by 1
- Monotone.locallyIntegrableproof · cited by 1