Theorems · Theorem · commutative algebra
LinearEquiv.smul_refl
∀ {R : Type u_1} {S : Type u_4} {M : Type u_5} [inst : Semiring R] [inst_1 : Semiring S] [inst_2 : AddCommMonoid M]
[inst_3 : Module R M] [inst_4 : Module S M] [inst_5 : SMulCommClass R S M] [inst_6 : SMul S R]
[inst_7 : IsScalarTower S R M] (α : Sˣ), α • LinearEquiv.refl R M = DistribMulAction.toLinearEquiv R M α- Defined in
- Mathlib.Algebra.Module.Equiv.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
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
- IsScalarTowerstatement and proof · cited by 3,896
- LinearEquivstatement · cited by 3,317
- Unitsstatement and proof · cited by 2,804
- SMulCommClassstatement and proof · cited by 1,927
- LinearEquiv.reflstatement · cited by 143
- SMulCommClass.symmstatement · cited by 67
- DistribMulAction.toLinearEquivstatement · cited by 8
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