Theorems · Theorem · nonassociative algebras

RootPairing.Base.IsPos.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] {P : RootPairing ι R M N} (b b_1 : P.Base),
  b = b_1 → ∀ [inst_5 : CharZero R] (i i_1 : ι), i = i_1 → b.IsPos i = b_1.IsPos i_1

Defined in: Mathlib.LinearAlgebra.RootSystem.Base
Cited by: 1 results in Mathlib
Foundations: Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing AddCommGroup Module AddCommGroup Module CharZero

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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
CharZerostatement and proof · cited by 932
RootPairingstatement and proof · cited by 710
RootPairing.Basestatement and proof · cited by 148
RootPairing.Base.IsPosstatement and proof · cited by 17

Cited by1

Results whose statement or proof uses this declaration.

RootPairing.Base.IsPos.add_zsmulproof · cited by 1