Theorems · Theorem · linear algebra

Submodule.finrank_span_eq_finrank

∀ {R : Type u_1} (A : Type u_2) {M : Type u_3} [inst : CommRing R] [inst_1 : CommRing A] [Nontrivial A]
  [inst_3 : Algebra R A] [Algebra.IsEpi R A] [Module.Flat R A] [inst_6 : AddCommGroup M] [inst_7 : Module R M]
  [inst_8 : Module A M] [IsScalarTower R A M] (p : Submodule R M) [Module.Free R ↥p] [Module.Finite R ↥p],
  Module.finrank A ↥(Submodule.span A ↑p) = Module.finrank R ↥p

Defined in: Mathlib.LinearAlgebra.Span.TensorProduct
Cited by: 1 results in Mathlib
Foundations: Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing CommRing Nontrivial Algebra Algebra.IsEpi Module.Flat AddCommGroup Module Module IsScalarTower Module.Free Module.Finite

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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
Algebrastatement and proof · cited by 11,388
SetLike.coestatement and proof · cited by 8,199
Submodulestatement and proof · cited by 7,192
IsScalarTowerstatement and proof · cited by 3,896
Nontrivialstatement and proof · cited by 2,416
Module.finrankstatement and proof · cited by 1,770
Submodule.spanstatement and proof · cited by 1,504
Module.Basisproof · cited by 1,477
Fintype.cardproof · cited by 1,386

Cited by1

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Submodule.finrank_span_eq_finrank_spanproof · cited by 1