Theorems · Theorem · nonassociative algebras

RootPairing.root_mem_submodule_iff_of_add_mem_invtSubmodule

∀ {ι : Type u_1} {M : Type u_3} {N : Type u_4} [inst : AddCommGroup M] [inst_1 : AddCommGroup N] {i j : ι}
  {K : Type u_5} [inst_2 : Field K] [NeZero 2] [inst_4 : Module K M] [inst_5 : Module K N] {P : RootPairing ι K M N}
  (q : ↥P.invtRootSubmodule), P.root i + P.root j ∈ Set.range ⇑P.root → (P.root i ∈ ↑q ↔ P.root j ∈ ↑q)

Defined in: Mathlib.LinearAlgebra.RootSystem.Finite.Lemmas
Cited by: 0 results in Mathlib
Foundations: Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: AddCommGroup AddCommGroup Field NeZero Module Module

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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
Fieldstatement and proof · cited by 7,404
Submodulestatement and proof · cited by 7,192
Set.rangestatement and proof · cited by 4,705
add_zeroproof · cited by 2,707
add_commproof · cited by 1,535
eq_or_neproof · cited by 1,117
Function.Embeddingstatement · cited by 988
map_addproof · cited by 964

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