Theorems · Theorem · linear algebra

LinearMap.rank_finsetSum_le

∀ {K : Type u} {V : Type v} {V' : Type v'} [inst : DivisionRing K] [inst_1 : AddCommGroup V] [inst_2 : Module K V]
  [inst_3 : AddCommGroup V'] [inst_4 : Module K V'] {η : Type u_1} (s : Finset η) (f : η → V →ₗ[K] V'),
  (∑ d ∈ s, f d).rank ≤ ∑ d ∈ s, (f d).rank

Defined in

Mathlib.LinearAlgebra.Dimension.LinearMap

Cited by

1 results in Mathlib

Foundations

Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingAddCommGroupModuleAddCommGroupModule