Theorems · Theorem · ring theory

LinearMap.restrictScalars_add

∀ {R : Type u_14} {S : Type u_15} {M : Type u_16} {N : Type u_17} [inst : Semiring R] [inst_1 : Semiring S]
  [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid N] [inst_4 : Module R M] [inst_5 : Module R N]
  [inst_6 : Module S M] [inst_7 : Module S N] [inst_8 : LinearMap.CompatibleSMul M N R S] (f g : M →ₗ[S] N),
  ↑R (f + g) = ↑R f + ↑R g

Defined in: Mathlib.Algebra.Module.LinearMap.Defs
Cited by: 0 results in Mathlib
Foundations: Depth 25 from the axioms · uses propext, Quot.sound
Assumes: Semiring Semiring AddCommMonoid AddCommMonoid Module Module Module Module LinearMap.CompatibleSMul

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Modulestatement and proof · cited by 20,661
RingHom.idstatement and proof · cited by 18,349
Semiringstatement and proof · cited by 13,802
AddCommMonoidstatement and proof · cited by 12,281
LinearMapstatement and proof · cited by 10,215
LinearMap.restrictScalarsstatement · cited by 215
LinearMap.CompatibleSMulstatement and proof · cited by 86

Cited by1

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LinearMap.restrictScalarsₗproof · cited by 7