Theorems · Theorem · linear algebra

LinearMap.finrank_eq_of_isPerfPair

∀ {K : Type u_1} {L : Type u_2} {M : Type u_3} {N : Type u_4} [inst : Field K] [inst_1 : Field L] [inst_2 : Algebra K L]
  [inst_3 : AddCommGroup M] [inst_4 : AddCommGroup N] [inst_5 : Module L M] [inst_6 : Module L N] [inst_7 : Module K M]
  [inst_8 : Module K N] [IsScalarTower K L M] (p : M →ₗ[L] N →ₗ[L] L) [p.IsPerfPair] (M' : Submodule K M)
  (N' : Submodule K N),
  Submodule.span L ↑M' = ⊤ →
    Submodule.span L ↑N' = ⊤ →
      (∀ x ∈ M', ∀ y ∈ N', (p x) y ∈ (algebraMap K L).range) → Module.finrank K ↥M' = Module.finrank L M

Defined in

Mathlib.LinearAlgebra.PerfectPairing.Restrict

Cited by

1 results in Mathlib

Foundations

Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldFieldAlgebraAddCommGroupAddCommGroupModuleModuleModuleModuleIsScalarTowerLinearMap.IsPerfPair