Theorems · Theorem · linear algebra

Submodule.mem_map_equiv

∀ {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] {τ₁₂ : R →+* R₂}
  {τ₂₁ : R₂ →+* R} [inst_6 : RingHomInvPair τ₁₂ τ₂₁] [inst_7 : RingHomInvPair τ₂₁ τ₁₂] (p : Submodule R M)
  {e : M ≃ₛₗ[τ₁₂] M₂} {x : M₂}, x ∈ Submodule.map (↑e) p ↔ e.symm x ∈ p

Defined in

Mathlib.Algebra.Module.Submodule.Map

Cited by

3 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Quot.sound

Assumes

SemiringSemiringAddCommMonoidAddCommMonoidModuleModuleRingHomInvPairRingHomInvPair