Theorems · Theorem · order theory

map_nonneg

∀ {F : Type u_1} {α : Type u_2} {β : Type u_3} [inst : FunLike F α β] [inst_1 : Preorder α] [inst_2 : Zero α]
  [inst_3 : Preorder β] [inst_4 : Zero β] [OrderHomClass F α β] [ZeroHomClass F α β] (f : F) {a : α}, 0 ≤ a → 0 ≤ f a

See also NonnegHomClass.apply_nonneg.

Defined in

Mathlib.Algebra.Order.Hom.Monoid

Cited by

4 results in Mathlib

Foundations

Depth 6 from the axioms · uses no axioms

Assumes

FunLikePreorderZeroPreorderZeroOrderHomClassZeroHomClass