Theorems · Theorem · order theory
Monotone.le_csInf_image
∀ {α : Type u_1} {β : Type u_2} [inst : ConditionallyCompleteLattice β] [inst_1 : Preorder α] {f : α → β},
Monotone f → ∀ {s : Set α}, s.Nonempty → ∀ {B : α}, B ∈ lowerBounds s → f B ≤ sInf (f '' s)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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.imagestatement · cited by 5,609
- Set.Nonemptystatement and proof · cited by 2,627
- Monotonestatement and proof · cited by 1,397
- InfSet.sInfstatement · cited by 935
- ConditionallyCompleteLatticestatement and proof · cited by 364
- lowerBoundsstatement and proof · cited by 212
- Set.Nonempty.imageproof · cited by 87
- le_csInfproof · cited by 36
- Monotone.mem_lowerBounds_imageproof · cited by 11
Cited by2
Results whose statement or proof uses this declaration.
- Monotone.map_csInf_le_csInf_imageproof · cited by 1
- sInf_within_of_ordConnectedproof · cited by 0