Theorems · Theorem · linear algebra

Module.Basis.card_le_card_of_submodule

∀ {R : Type u} {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {ι : Type w}
  {ι' : Type w'} [StrongRankCondition R] (N : Submodule R M) [inst_4 : Fintype ι] (b : Module.Basis ι R M)
  [inst_5 : Fintype ι'] (b' : Module.Basis ι' R ↥N), Fintype.card ι' ≤ Fintype.card ι

Defined in

Mathlib.LinearAlgebra.Dimension.StrongRankCondition

Cited by

0 results in Mathlib

Foundations

Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModuleStrongRankConditionFintypeFintype