Theorems · Theorem · nonassociative algebras

RootPairing.Base.cartanMatrixIn.congr_simp

∀ {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] (S : Type u_5) [inst_5 : CommRing S]
  [inst_6 : Algebra S R] {P : RootPairing ι R M N} [inst_7 : P.IsValuedIn S] (b : P.Base) (a a_1 : ↥b.support),
  a = a_1 →
    ∀ (a_2 a_3 : ↥b.support),
      a_2 = a_3 → RootPairing.Base.cartanMatrixIn S b a a_2 = RootPairing.Base.cartanMatrixIn S b a_1 a_3

Defined in

Mathlib.LinearAlgebra.RootSystem.CartanMatrix

Cited by

0 results in Mathlib

Foundations

Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleCommRingAlgebraRootPairing.IsValuedIn