Theorems · Theorem · linear algebra
Submodule.Quotient.restrictScalarsEquiv_symm_mk
∀ {R : Type u_1} {M : Type u_2} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] (S : Type u_3)
[inst_3 : Ring S] [inst_4 : SMul S R] [inst_5 : Module S M] [inst_6 : IsScalarTower S R M] (P : Submodule R M)
(x : M), (Submodule.Quotient.restrictScalarsEquiv S P).symm (Submodule.Quotient.mk x) = Submodule.Quotient.mk x- Defined in
- Mathlib.LinearAlgebra.Quotient.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
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
- AddCommGroupstatement and proof · cited by 12,871
- Ringstatement and proof · cited by 7,463
- Submodulestatement and proof · cited by 7,192
- IsScalarTowerstatement and proof · cited by 3,896
- LinearEquivstatement · cited by 3,317
- HasQuotient.Quotientstatement · cited by 2,301
- LinearEquiv.symmstatement · cited by 1,461
- Submodule.Quotient.mkstatement · cited by 184
- Submodule.restrictScalarsstatement · cited by 180
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