Theorems · Theorem · nonassociative algebras

RootPairing.invtRootSubmodule.eq_top_iff

∀ {ι : Type u_1} {M : Type u_3} {N : Type u_4} [inst : AddCommGroup M] [inst_1 : AddCommGroup N] {K : Type u_5}
  [inst_2 : Field K] [inst_3 : Module K M] [inst_4 : Module K N] {P : RootPairing ι K M N} [P.IsRootSystem]
  (q : ↥P.invtRootSubmodule), q = ⊤ ↔ Set.range ⇑P.root ⊆ ↑↑q

Defined in: Mathlib.LinearAlgebra.RootSystem.Irreducible
Cited by: 0 results in Mathlib
Foundations: Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: AddCommGroup AddCommGroup Field Module Module RootPairing.IsRootSystem

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DFunLike.coestatement and proof · cited by 62,936
Setstatement · cited by 53,352
Modulestatement and proof · cited by 20,661
AddCommGroupstatement and proof · cited by 12,871
Top.topstatement and proof · cited by 9,680
SetLike.coestatement and proof · cited by 8,199
Fieldstatement and proof · cited by 7,404
Submodulestatement and proof · cited by 7,192
Set.rangestatement and proof · cited by 4,705
Function.Embeddingstatement · cited by 988
RootPairingstatement and proof · cited by 710
RootPairing.rootstatement and proof · cited by 326

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