Theorems · Theorem · order theory
Covariant.monotone_of_const
∀ {M : Type u_1} {N : Type u_2} {μ : M → N → N} [inst : Preorder N] [CovariantClass M N μ fun x1 x2 => x1 ≤ x2] (m : M),
Monotone (μ m)The partial application of a constant to a covariant operator is monotone.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 3 from the axioms · uses no axioms
- Assumes
- PreorderCovariantClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Monotonestatement · cited by 1,397
- CovariantClassstatement and proof · cited by 25
- CovariantClass.elimproof · cited by 22
Cited by3
Results whose statement or proof uses this declaration.
- Monotone.covariant_of_constproof · cited by 1
- Antitone.covariant_of_constproof · cited by 1
- not_summable_indicator_mod_of_antitone_of_negproof · cited by 1