Theorems · Theorem · ring theory

LinearMap.congr_fun

∀ {R : Type u_1} {S : Type u_5} {M : Type u_8} {M₃ : Type u_11} [inst : Semiring R] [inst_1 : Semiring S]
  [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₃] [inst_4 : Module R M] [inst_5 : Module S M₃] {σ : R →+* S}
  {f g : M →ₛₗ[σ] M₃}, f = g → ∀ (x : M), f x = g x

If two linear maps are equal, they are equal at each point.

Defined in

Mathlib.Algebra.Module.LinearMap.Defs

Cited by

96 results in Mathlib

Foundations

Depth 21 from the axioms, rests on 151 definitions · uses no axioms

Assumes

SemiringSemiringAddCommMonoidAddCommMonoidModuleModule