Theorems · Theorem · order theory
Monotone.csSup_image_le
∀ {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 ∈ upperBounds s → sSup (f '' s) ≤ f B- 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
- SupSet.sSupstatement · cited by 954
- ConditionallyCompleteLatticestatement and proof · cited by 364
- upperBoundsstatement and proof · cited by 263
- Set.Nonempty.imageproof · cited by 87
- csSup_leproof · cited by 35
- Monotone.mem_upperBounds_imageproof · cited by 12
Cited by2
Results whose statement or proof uses this declaration.
- Monotone.csSup_image_le_map_csSupproof · cited by 1
- sSup_within_of_ordConnectedproof · cited by 0