Mathlib Map

Theorems · Theorem · order theory

PositiveLinearMap.toLinearMap_injective

∀ {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], Function.Injective PositiveLinearMap.toLinearMap
Defined in
Mathlib.Algebra.Order.Module.PositiveLinearMap
Cited by
1 results in Mathlib
Foundations
Depth 24 from the axioms · uses Quot.sound
Assumes
SemiringAddCommMonoidPartialOrderAddCommMonoidPartialOrderModuleModule
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Around this declaration

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

PositiveLinearMap.toLinearMap_inj · cited by 0PositiveLinearMap.toLinea…DFunLike.coe · cited by 62936DFunLike.coeModule · cited by 20661ModuleRingHom.id · cited by 18349RingHom.idSemiring · cited by 13802SemiringAddCommMonoid · cited by 12281AddCommMonoidLinearMap · cited by 10215LinearMapPartialOrder · cited by 6410PartialOrderPositiveLinearMap · cited by 52PositiveLinearMapPositiveLinearMap.toLinearMap · cited by 12PositiveLinearMap.toLinea…PositiveLinearMap.ext · cited by 4PositiveLinearMap.extPositiveLinearMap.toLinearMap…CITED BYCITES

Cites10

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Cited by1

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