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Theorems · Theorem · order theory

OrderMonoidHom.comp_apply

∀ {α : Type u_2} {β : Type u_3} {γ : Type u_4} [inst : Preorder α] [inst_1 : Preorder β] [inst_2 : Preorder γ]
  [inst_3 : MulOneClass α] [inst_4 : MulOneClass β] [inst_5 : MulOneClass γ] (f : β →*o γ) (g : α →*o β) (a : α),
  (f.comp g) a = f (g a)
Defined in
Mathlib.Algebra.Order.Hom.Monoid
Cited by
1 results in Mathlib
Foundations
Depth 15 from the axioms · uses propext, Quot.sound
Assumes
PreorderPreorderPreorderMulOneClassMulOneClassMulOneClass
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

OrderMonoidHom.cancel_left · cited by 0OrderMonoidHom.cancel_leftDFunLike.coe · cited by 62936DFunLike.coePreorder · cited by 7952PreorderMulOneClass · cited by 1018MulOneClassOrderMonoidHom · cited by 67OrderMonoidHomOrderMonoidHom.comp · cited by 20OrderMonoidHom.compOrderMonoidHom.comp_applyCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.