Theorems · Theorem · order theory
MonotoneOn.sSup_image_Icc
∀ {α : Type u_1} {β : Type u_2} [inst : Preorder α] [inst_1 : ConditionallyCompleteLattice β] {f : α → β} {a b : α},
b ≤ a → MonotoneOn f (Set.Icc b a) → sSup (f '' Set.Icc b a) = f a- Cited by
- 1 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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.imagestatement and proof · cited by 5,609
- Set.Iccstatement and proof · cited by 1,702
- SupSet.sSupstatement · cited by 954
- ConditionallyCompleteLatticestatement and proof · cited by 364
- MonotoneOnstatement and proof · cited by 311
- upperBoundsproof · cited by 263
- LE.le.trans'proof · cited by 140
- Set.Nonempty.imageproof · cited by 87
- Set.right_mem_Iccproof · cited by 60
- Std.ge_reflproof · cited by 23
- Set.nonempty_Iccproof · cited by 21
Cited by1
Results whose statement or proof uses this declaration.
- AntitoneOn.sSup_image_Iccproof · cited by 0