Theorems · Theorem · linear algebra
LinearEquiv.snd_comp_prodComm
∀ {R : Type u} {M : Type v} {M₂ : Type w} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : AddCommMonoid M₂]
[inst_3 : Module R M] [inst_4 : Module R M₂],
LinearMap.snd R M₂ M ∘ₗ ↑(LinearEquiv.prodComm R M M₂) = LinearMap.fst R M M₂- Defined in
- Mathlib.LinearAlgebra.Prod
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 36 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- LinearMapstatement · cited by 10,215
- LinearMap.compstatement · cited by 1,642
- LinearEquiv.toLinearMapstatement · cited by 1,171
- LinearMap.extproof · cited by 844
- LinearMap.fststatement · cited by 64
- LinearMap.sndstatement · cited by 61
- LinearEquiv.prodCommstatement · cited by 17
- LinearMap.prod_extproof · cited by 14
Cited by1
Results whose statement or proof uses this declaration.
- LinearPMap.inverse_rangeproof · cited by 0