Theorems · Theorem · nonassociative algebras

RootPairing.Hom.weightHom_injective

∀ {ι : Type u_1} {R : Type u_2} {M : Type u_3} {N : Type u_4} [inst : CommRing R] [inst_1 : AddCommGroup M]
  [inst_2 : Module R M] [inst_3 : AddCommGroup N] [inst_4 : Module R N] (P : RootPairing ι R M N),
  Function.Injective ⇑(RootPairing.Hom.weightHom P)

Defined in: Mathlib.LinearAlgebra.RootSystem.Hom
Cited by: 1 results in Mathlib
Foundations: Depth 50 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing AddCommGroup Module AddCommGroup Module

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

DFunLike.coestatement and proof · cited by 62,936
Modulestatement and proof · cited by 20,661
CommRingstatement and proof · cited by 17,173
AddCommGroupstatement and proof · cited by 12,871
MonoidHomstatement · cited by 3,629
LinearMap.extproof · cited by 844
Module.Endstatement · cited by 774
RootPairingstatement and proof · cited by 710
RootPairing.rootproof · cited by 326
LinearEquiv.injectiveproof · cited by 162
Function.Embedding.injectiveproof · cited by 111
RootPairing.toLinearMapproof · cited by 108

Cited by1

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RootPairing.Equiv.weightHom_injectiveproof · cited by 0