Theorems · Theorem · commutative algebra

SModEq.map

∀ {R : Type u_1} [inst : Ring R] {M : Type u_4} [inst_1 : AddCommGroup M] [inst_2 : Module R M] {U : Submodule R M}
  {x y : M} {N : Type u_5} [inst_3 : AddCommGroup N] [inst_4 : Module R N],
  x ≡ y [SMOD U] → ∀ (f : M →ₗ[R] N), f x ≡ f y [SMOD Submodule.map f U]

Defined in

Mathlib.LinearAlgebra.SModEq.Basic

Cited by

0 results in Mathlib

Foundations

Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleAddCommGroupModule