Theorems · Theorem · nonassociative algebras

RootPairing.restrictScalars_coe_coroot

∀ {ι : Type u_1} {L : Type u_2} {M : Type u_3} {N : Type u_4} [inst : Field L] [inst_1 : AddCommGroup M]
  [inst_2 : AddCommGroup N] [inst_3 : Module L M] [inst_4 : Module L N] (P : RootPairing ι L M N) (K : Type u_5)
  [inst_5 : Field K] [inst_6 : Algebra K L] [inst_7 : Module K M] [inst_8 : Module K N] [inst_9 : IsScalarTower K L M]
  [inst_10 : IsScalarTower K L N] [inst_11 : P.IsBalanced] [inst_12 : P.IsValuedIn K] (i : ι),
  ↑((P.restrictScalars' K).coroot i) = P.coroot i

Defined in: Mathlib.LinearAlgebra.RootSystem.BaseChange
Cited by: 0 results in Mathlib
Foundations: Depth 126 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field AddCommGroup AddCommGroup Module Module Field Algebra Module Module IsScalarTower IsScalarTower RootPairing.IsBalanced RootPairing.IsValuedIn

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DFunLike.coestatement · cited by 62,936
Modulestatement and proof · cited by 20,661
AddCommGroupstatement and proof · cited by 12,871
Algebrastatement and proof · cited by 11,388
Fieldstatement and proof · cited by 7,404
Submodulestatement · cited by 7,192
Set.rangestatement · cited by 4,705
IsScalarTowerstatement and proof · cited by 3,896
Submodule.spanstatement · cited by 1,504
Function.Embeddingstatement · cited by 988
RootPairingstatement and proof · cited by 710
RootPairing.rootstatement · cited by 326

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