Theorems · Theorem · linear algebra

LinearEquiv.range_comp

∀ {R : Type u_1} {R₂ : Type u_3} {R₃ : Type u_4} {M : Type u_5} {M₂ : Type u_7} {M₃ : Type u_8} [inst : Semiring R]
  [inst_1 : Semiring R₂] [inst_2 : Semiring R₃] [inst_3 : AddCommMonoid M] [inst_4 : AddCommMonoid M₂]
  [inst_5 : AddCommMonoid M₃] {module_M : Module R M} {module_M₂ : Module R₂ M₂} {module_M₃ : Module R₃ M₃}
  {σ₁₂ : R →+* R₂} {σ₂₁ : R₂ →+* R} {σ₂₃ : R₂ →+* R₃} {σ₁₃ : R →+* R₃} [inst_6 : RingHomCompTriple σ₁₂ σ₂₃ σ₁₃]
  {re₁₂ : RingHomInvPair σ₁₂ σ₂₁} {re₂₁ : RingHomInvPair σ₂₁ σ₁₂} (e : M ≃ₛₗ[σ₁₂] M₂) (h : M₂ →ₛₗ[σ₂₃] M₃)
  [inst_7 : RingHomSurjective σ₂₃] [inst_8 : RingHomSurjective σ₁₃], (h ∘ₛₗ ↑e).range = h.range

Defined in

Mathlib.Algebra.Module.Submodule.Equiv

Cited by

5 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringSemiringSemiringAddCommMonoidAddCommMonoidAddCommMonoidRingHomCompTripleRingHomSurjectiveRingHomSurjective