Theorems · Theorem · linear algebra

LinearMap.coe_restrict_apply

∀ {R : Type u_1} {R₂ : Type u_3} {M : Type u_5} {M₂ : Type u_7} [inst : Semiring R] [inst_1 : Semiring R₂]
  [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] [inst_4 : Module R M] [inst_5 : Module R₂ M₂] {σ₁₂ : R →+* R₂}
  {f : M →ₛₗ[σ₁₂] M₂} {p : Submodule R M} {q : Submodule R₂ M₂} (hf : ∀ x ∈ p, f x ∈ q) (x : ↥p),
  ↑((f.restrict hf) x) = f ↑x

Defined in

Mathlib.Algebra.Module.Submodule.LinearMap

Cited by

1 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Quot.sound

Assumes

SemiringSemiringAddCommMonoidAddCommMonoidModuleModule