Theorems · Theorem · nonassociative algebras

RootPairing.Base.height_ne_zero

∀ {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 : P.Base)
  [inst_5 : CharZero R] (i : ι), b.height i ≠ 0

Defined in: Mathlib.LinearAlgebra.RootSystem.Base
Cited by: 4 results in Mathlib
Foundations: Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing AddCommGroup Module AddCommGroup Module CharZero

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Cites25

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

DFunLike.coeproof · cited by 62,936
Modulestatement and proof · cited by 20,661
CommRingstatement and proof · cited by 17,173
AddCommGroupstatement and proof · cited by 12,871
SetLike.coeproof · cited by 8,199
Finset.sumproof · cited by 5,195
Finset.sum_congrproof · cited by 2,323
LT.lt.leproof · cited by 2,189
le_antisymmproof · cited by 2,068
LT.lt.ne'proof · cited by 1,417
CharZerostatement and proof · cited by 932
LT.lt.neproof · cited by 872

Cited by4

Results whose statement or proof uses this declaration.

RootPairing.Base.IsPos.or_negproof · cited by 3
RootPairing.Base.isPos_iff'proof · cited by 3
RootPairing.Base.IsPos.induction_on_addproof · cited by 2
RootPairing.Base.IsPos.neg_iff_notproof · cited by 0