Theorems · Theorem · order theory
Monotone.map_max
∀ {α : Type u} {β : Type v} [inst : LinearOrder α] [inst_1 : LinearOrder β] {f : α → β} {a b : α},
Monotone f → f (max a b) = max (f a) (f b)- Defined in
- Mathlib.Order.MinMax
- Cited by
- 55 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext
- Assumes
- LinearOrderLinearOrder
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.
- LinearOrderstatement and proof · cited by 8,572
- Monotonestatement and proof · cited by 1,397
- le_totalproof · cited by 294
- sup_of_le_leftproof · cited by 218
- sup_of_le_rightproof · cited by 143
Cited by55
Results whose statement or proof uses this declaration.
- Cardinal.lift_maxproof · cited by 16
- NNReal.coe_maxproof · cited by 11
- Nat.cast_maxproof · cited by 10
- mul_max_of_nonnegproof · cited by 10
- max_mul_of_nonnegproof · cited by 7
- min_neg_negproof · cited by 4
- LipschitzWith.prodMkproof · cited by 4
- max_mulproof · cited by 3
- Fin.image_addNat_uIccproof · cited by 3
- max_div_div_rightproof · cited by 2
- Cardinal.aleph_maxproof · cited by 2
- mul_maxproof · cited by 2