Mathlib Map

Theorems · Theorem · order theory

PositiveLinearMap.id_comp

∀ {R : Type u_1} {E₁ : Type u_2} {E₂ : Type u_3} [inst : Semiring R] [inst_1 : AddCommMonoid E₁]
  [inst_2 : PartialOrder E₁] [inst_3 : AddCommMonoid E₂] [inst_4 : PartialOrder E₂] [inst_5 : Module R E₁]
  [inst_6 : Module R E₂] (f : E₁ →ₚ[R] E₂), (PositiveLinearMap.id R E₂).comp f = f
Defined in
Mathlib.Algebra.Order.Module.PositiveLinearMap
Cited by
0 results in Mathlib
Foundations
Depth 25 from the axioms · uses propext, Quot.sound
Assumes
SemiringAddCommMonoidPartialOrderAddCommMonoidPartialOrderModuleModule
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Module · cited by 20661ModuleSemiring · cited by 13802SemiringAddCommMonoid · cited by 12281AddCommMonoidPartialOrder · cited by 6410PartialOrderPositiveLinearMap · cited by 52PositiveLinearMapPositiveLinearMap.comp · cited by 5PositiveLinearMap.compPositiveLinearMap.id · cited by 5PositiveLinearMap.idPositiveLinearMap.id_compCITED BYCITES

Cites7

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

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.