Theorems · Theorem · nonassociative algebras

RootPairing.toInvariantForm_form

∀ {ι : Type u_1} {R : Type u_2} {M : Type u_3} {N : Type u_4} [inst : Fintype ι] [inst_1 : AddCommGroup M]
  [inst_2 : AddCommGroup N] [inst_3 : CommRing R] [inst_4 : Module R M] [inst_5 : Module R N] (P : RootPairing ι R M N)
  [inst_6 : P.IsAnisotropic], P.toInvariantForm.form = P.RootForm

Defined in: Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate
Cited by: 3 results in Mathlib
Foundations: Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Fintype AddCommGroup AddCommGroup CommRing Module Module RootPairing.IsAnisotropic

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Cites10

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

Modulestatement and proof · cited by 20,661
CommRingstatement and proof · cited by 17,173
AddCommGroupstatement and proof · cited by 12,871
Fintypestatement and proof · cited by 7,736
RootPairingstatement and proof · cited by 710
LinearMap.BilinFormstatement · cited by 501
RootPairing.RootFormstatement · cited by 41
RootPairing.InvariantForm.formstatement and proof · cited by 33
RootPairing.IsAnisotropicstatement and proof · cited by 31
RootPairing.toInvariantFormstatement and proof · cited by 6

Cited by3

Results whose statement or proof uses this declaration.

RootPairing.Base.cartanMatrix_mul_diagonal_eqproof · cited by 1
RootPairing.polarizationEquiv_toLinearMapproof · cited by 1
RootPairing.smul_coroot_eq_of_root_add_root_eqproof · cited by 0