File: Mathlib/Algebra/Module/ULift.lean

full_name: ULift.vaddLeft
code: @[to_additive]
instance smulLeft [SMul R M] : SMul (ULift R) M 
goal: VAdd (ULift.{u_1, u} R) M

full_name: ULift.smulLeft
code: @[to_additive]
instance smulLeft [SMul R M] : SMul (ULift R) M 
goal: SMul (ULift.{u_1, u} R) M

full_name: ULift.vadd_def
code: @[to_additive (attr := simp)]
theorem smul_def [SMul R M] (s : ULift R) (x : M) : s • x = s.down • x 
goal: s +ᵥ x = s.down +ᵥ x

full_name: ULift.smul_def
code: @[to_additive (attr := simp)]
theorem smul_def [SMul R M] (s : ULift R) (x : M) : s • x = s.down • x 
goal: s • x = s.down • x

full_name: ULift.isScalarTower
code: instance isScalarTower [SMul R M] [SMul M N] [SMul R N] [IsScalarTower R M N] :
    IsScalarTower (ULift R) M N 
goal: IsScalarTower (ULift.{u_1, u} R) M N

full_name: ULift.isScalarTower'
code: instance isScalarTower' [SMul R M] [SMul M N] [SMul R N] [IsScalarTower R M N] :
    IsScalarTower R (ULift M) N 
goal: IsScalarTower R (ULift.{u_1, v} M) N

full_name: ULift.isScalarTower''
code: instance isScalarTower'' [SMul R M] [SMul M N] [SMul R N] [IsScalarTower R M N] :
    IsScalarTower R M (ULift N) 
goal: IsScalarTower R M (ULift.{u_1, w} N)

full_name: ULift.instIsCentralScalar
code: instance [SMul R M] [SMul Rᵐᵒᵖ M] [IsCentralScalar R M] : IsCentralScalar R (ULift M) 
goal: IsCentralScalar R (ULift.{u_1, v} M)

full_name: ULift.addAction
code: @[to_additive]
instance mulAction [Monoid R] [MulAction R M] : MulAction (ULift R) M 
goal: AddAction (ULift.{u_1, u} R) M

full_name: ULift.mulAction
code: @[to_additive]
instance mulAction [Monoid R] [MulAction R M] : MulAction (ULift R) M 
goal: MulAction (ULift.{u_1, u} R) M

full_name: ULift.mulAction'
code: @[to_additive]
instance mulAction' [Monoid R] [MulAction R M] : MulAction R (ULift M) 
goal: MulAction R (ULift.{u_1, v} M)

full_name: ULift.addAction'
code: @[to_additive]
instance mulAction' [Monoid R] [MulAction R M] : MulAction R (ULift M) 
goal: AddAction R (ULift.{u_1, v} M)

full_name: ULift.smulZeroClass
code: instance smulZeroClass [Zero M] [SMulZeroClass R M] : SMulZeroClass (ULift R) M 
goal: SMulZeroClass (ULift.{u_1, u} R) M

full_name: ULift.smulZeroClass'
code: instance smulZeroClass' [Zero M] [SMulZeroClass R M] : SMulZeroClass R (ULift M) 
goal: SMulZeroClass R (ULift.{u_1, v} M)

full_name: ULift.distribSMul
code: instance distribSMul [AddZeroClass M] [DistribSMul R M] : DistribSMul (ULift R) M 
goal: DistribSMul (ULift.{u_1, u} R) M

full_name: ULift.distribSMul'
code: instance distribSMul' [AddZeroClass M] [DistribSMul R M] : DistribSMul R (ULift M) 
goal: DistribSMul R (ULift.{u_1, v} M)

full_name: ULift.distribMulAction
code: instance distribMulAction [Monoid R] [AddMonoid M] [DistribMulAction R M] :
    DistribMulAction (ULift R) M 
goal: DistribMulAction (ULift.{u_1, u} R) M

full_name: ULift.distribMulAction'
code: instance distribMulAction' [Monoid R] [AddMonoid M] [DistribMulAction R M] :
    DistribMulAction R (ULift M) 
goal: DistribMulAction R (ULift.{u_1, v} M)

full_name: ULift.mulDistribMulAction
code: instance mulDistribMulAction [Monoid R] [Monoid M] [MulDistribMulAction R M] :
    MulDistribMulAction (ULift R) M 
goal: MulDistribMulAction (ULift.{u_1, u} R) M

full_name: ULift.mulDistribMulAction'
code: instance mulDistribMulAction' [Monoid R] [Monoid M] [MulDistribMulAction R M] :
    MulDistribMulAction R (ULift M) 
goal: MulDistribMulAction R (ULift.{u_1, v} M)

full_name: ULift.smulWithZero
code: instance smulWithZero [Zero R] [Zero M] [SMulWithZero R M] : SMulWithZero (ULift R) M 
goal: SMulWithZero (ULift.{u_1, u} R) M

full_name: ULift.smulWithZero'
code: instance smulWithZero' [Zero R] [Zero M] [SMulWithZero R M] : SMulWithZero R (ULift M) 
goal: SMulWithZero R (ULift.{u_1, v} M)

full_name: ULift.mulActionWithZero
code: instance mulActionWithZero [MonoidWithZero R] [Zero M] [MulActionWithZero R M] :
    MulActionWithZero (ULift R) M 
goal: MulActionWithZero (ULift.{u_1, u} R) M

full_name: ULift.mulActionWithZero'
code: instance mulActionWithZero' [MonoidWithZero R] [Zero M] [MulActionWithZero R M] :
    MulActionWithZero R (ULift M) 
goal: MulActionWithZero R (ULift.{u_1, v} M)

full_name: ULift.module
code: instance module [Semiring R] [AddCommMonoid M] [Module R M] : Module (ULift R) M 
goal: Module (ULift.{u_1, u} R) M

full_name: ULift.module'
code: instance module' [Semiring R] [AddCommMonoid M] [Module R M] : Module R (ULift M) 
goal: Module R (ULift.{u_1, v} M)

full_name: ULift.moduleEquiv_apply
code: /-- The `R`-linear equivalence between `ULift M` and `M`.

This is a linear version of `AddEquiv.ulift`. -/
@[simps apply symm_apply]
def moduleEquiv [Semiring R] [AddCommMonoid M] [Module R M] : ULift.{w} M ≃ₗ[R] M 
goal: ULift.moduleEquiv self = self.down

full_name: ULift.moduleEquiv
code: /-- The `R`-linear equivalence between `ULift M` and `M`.

This is a linear version of `AddEquiv.ulift`. -/
@[simps apply symm_apply]
def moduleEquiv [Semiring R] [AddCommMonoid M] [Module R M] : ULift.{w} M ≃ₗ[R] M 
goal: ULift.{w, v} M ≃ₗ[R] M

full_name: ULift.moduleEquiv_symm_apply
code: /-- The `R`-linear equivalence between `ULift M` and `M`.

This is a linear version of `AddEquiv.ulift`. -/
@[simps apply symm_apply]
def moduleEquiv [Semiring R] [AddCommMonoid M] [Module R M] : ULift.{w} M ≃ₗ[R] M 
goal: ULift.moduleEquiv.symm down = { down := down }