Theorems · Theorem · nonassociative algebras

RootPairing.mapsTo_coreflection_coroot

∀ {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) (i : ι),
  Set.MapsTo (⇑(P.coreflection i)) (Set.range ⇑P.coroot) (Set.range ⇑P.coroot)

Defined in: Mathlib.LinearAlgebra.RootSystem.Defs
Cited by: 1 results in Mathlib
Foundations: Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing AddCommGroup Module AddCommGroup Module

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Cites15

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
RingHom.idstatement · cited by 18,349
CommRingstatement and proof · cited by 17,173
AddCommGroupstatement and proof · cited by 12,871
Set.rangestatement and proof · cited by 4,705
LinearEquivstatement · cited by 3,317
Function.Embeddingstatement · cited by 988
Set.MapsTostatement · cited by 732
RootPairingstatement and proof · cited by 710
Set.mem_range_selfproof · cited by 328
RootPairing.corootstatement and proof · cited by 123

Cited by1

Results whose statement or proof uses this declaration.

RootPairing.smul_coroot_eq_of_root_eq_smulproof · cited by 1