Theorems · Theorem · linear algebra

LinearMap.exists_ne_zero_of_sSup_eq

∀ {R : Type u_1} {R₂ : Type u_2} {M : Type u_4} {M₂ : Type u_5} [inst : Semiring R] [inst_1 : AddCommMonoid M]
  [inst_2 : Module R M] [inst_3 : Semiring R₂] {σ₁₂ : R →+* R₂} [inst_4 : AddCommMonoid M₂] [inst_5 : Module R₂ M₂]
  {N : Submodule R M} {f : ↥N →ₛₗ[σ₁₂] M₂},
  f ≠ 0 → ∀ (s : Set (Submodule R M)) (hs : sSup s = N), ∃ m, ∃ (h : m ∈ s), f ∘ₛₗ Submodule.inclusion ⋯ ≠ 0

Defined in

Mathlib.LinearAlgebra.Span.Basic

Cited by

0 results in Mathlib

Foundations

Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModuleSemiringAddCommMonoidModule