Theorems · Theorem · linear algebra
Module.Basis.repr_unop_eq_mulOpposite_repr
∀ {R : Type u_1} {H : Type u_2} {ι : Type u_3} [inst : Semiring R] [inst_1 : AddCommMonoid H] [inst_2 : Module R H]
(b : Module.Basis ι R H) (x : Hᵐᵒᵖ), b.repr (MulOpposite.unop x) = b.mulOpposite.repr x- Defined in
- Mathlib.LinearAlgebra.Basis.MulOpposite
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- 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
- Finsuppstatement · cited by 5,255
- LinearEquivstatement · cited by 3,317
- Module.Basisstatement and proof · cited by 1,477
- MulOppositestatement and proof · cited by 1,135
- Module.Basis.reprstatement · cited by 498
- MulOpposite.unopstatement · cited by 268
- Module.Basis.mulOppositestatement · cited by 7
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