File: Mathlib/Logic/Small/Group.lean

full_name: instZeroShrink
code: instance [Zero α] [Small α] : Zero (Shrink α) 
goal: Zero (Shrink.{u_2, u_1} α)

full_name: instOneShrink
code: @[to_additive existing]
instance [One α] [Small α] : One (Shrink α) 
goal: One (Shrink.{u_2, u_1} α)

full_name: equivShrink_symm_zero
code: @[simp]
lemma equivShrink_symm_zero [Zero α] [Small α] : (equivShrink α).symm 0 = 0 
goal: (equivShrink α).symm 0 = 0

full_name: equivShrink_symm_one
code: @[to_additive existing (attr := simp)]
lemma equivShrink_symm_one [One α] [Small α] : (equivShrink α).symm 1 = 1 
goal: (equivShrink α).symm 1 = 1

full_name: instAddShrink
code: instance [Add α] [Small α] : Add (Shrink α) 
goal: Add (Shrink.{u_2, u_1} α)

full_name: instMulShrink
code: @[to_additive existing]
instance [Mul α] [Small α] : Mul (Shrink α) 
goal: Mul (Shrink.{u_2, u_1} α)

full_name: equivShrink_symm_add
code: @[simp]
lemma equivShrink_symm_add [Add α] [Small α] (x y : Shrink α) :
    (equivShrink α).symm (x + y) = (equivShrink α).symm x + (equivShrink α).symm y 
goal: (equivShrink α).symm (x + y) = (equivShrink α).symm x + (equivShrink α).symm y

full_name: equivShrink_add
code: @[simp]
lemma equivShrink_add [Add α] [Small α] (x y : α) :
    equivShrink α (x + y) = equivShrink α x + equivShrink α y 
goal: (equivShrink α) (x + y) = (equivShrink α) x + (equivShrink α) y

full_name: equivShrink_symm_mul
code: @[to_additive existing (attr := simp)]
lemma equivShrink_symm_mul [Mul α] [Small α] (x y : Shrink α) :
    (equivShrink α).symm (x * y) = (equivShrink α).symm x * (equivShrink α).symm y 
goal: (equivShrink α).symm (x * y) = (equivShrink α).symm x * (equivShrink α).symm y

full_name: equivShrink_mul
code: @[to_additive existing (attr := simp)]
lemma equivShrink_mul [Mul α] [Small α] (x y : α) :
    equivShrink α (x * y) = equivShrink α x * equivShrink α y 
goal: (equivShrink α) (x * y) = (equivShrink α) x * (equivShrink α) y

full_name: instSubShrink
code: instance [Sub α] [Small α] : Sub (Shrink α) 
goal: Sub (Shrink.{u_2, u_1} α)

full_name: instDivShrink
code: @[to_additive existing]
instance [Div α] [Small α] : Div (Shrink α) 
goal: Div (Shrink.{u_2, u_1} α)

full_name: equivShrink_symm_sub
code: @[simp]
lemma equivShrink_symm_sub [Sub α] [Small α] (x y : Shrink α) :
    (equivShrink α).symm (x - y) = (equivShrink α).symm x - (equivShrink α).symm y 
goal: (equivShrink α).symm (x - y) = (equivShrink α).symm x - (equivShrink α).symm y

full_name: equivShrink_sub
code: @[simp]
lemma equivShrink_sub [Sub α] [Small α] (x y : α) :
    equivShrink α (x - y) = equivShrink α x - equivShrink α y 
goal: (equivShrink α) (x - y) = (equivShrink α) x - (equivShrink α) y

full_name: equivShrink_symm_div
code: @[to_additive existing (attr := simp)]
lemma equivShrink_symm_div [Div α] [Small α] (x y : Shrink α) :
    (equivShrink α).symm (x / y) = (equivShrink α).symm x / (equivShrink α).symm y 
goal: (equivShrink α).symm (x / y) = (equivShrink α).symm x / (equivShrink α).symm y

full_name: equivShrink_div
code: @[to_additive existing (attr := simp)]
lemma equivShrink_div [Div α] [Small α] (x y : α) :
    equivShrink α (x / y) = equivShrink α x / equivShrink α y 
goal: (equivShrink α) (x / y) = (equivShrink α) x / (equivShrink α) y

full_name: instNegShrink
code: instance [Neg α] [Small α] : Neg (Shrink α) 
goal: Neg (Shrink.{u_2, u_1} α)

full_name: instInvShrink
code: @[to_additive existing]
instance [Inv α] [Small α] : Inv (Shrink α) 
goal: Inv (Shrink.{u_2, u_1} α)

full_name: equivShrink_symm_neg
code: @[simp]
lemma equivShrink_symm_neg [Neg α] [Small α] (x : Shrink α) :
    (equivShrink α).symm (-x) = -(equivShrink α).symm x 
goal: (equivShrink α).symm (-x) = -(equivShrink α).symm x

full_name: equivShrink_neg
code: @[simp]
lemma equivShrink_neg [Neg α] [Small α] (x : α) :
    equivShrink α (-x) = -equivShrink α x 
goal: (equivShrink α) (-x) = -(equivShrink α) x

full_name: equivShrink_symm_inv
code: @[to_additive existing (attr := simp)]
lemma equivShrink_symm_inv [Inv α] [Small α] (x : Shrink α) :
    (equivShrink α).symm x⁻¹ = ((equivShrink α).symm x)⁻¹ 
goal: (equivShrink α).symm x⁻¹ = ((equivShrink α).symm x)⁻¹

full_name: equivShrink_inv
code: @[to_additive existing (attr := simp)]
lemma equivShrink_inv [Inv α] [Small α] (x : α) :
    equivShrink α x⁻¹ = (equivShrink α x)⁻¹ 
goal: (equivShrink α) x⁻¹ = ((equivShrink α) x)⁻¹

full_name: instAddSemigroupShrink
code: instance [AddSemigroup α] [Small α] : AddSemigroup (Shrink α) 
goal: AddSemigroup (Shrink.{u_2, u_1} α)

full_name: instSemigroupShrink
code: @[to_additive existing]
instance [Semigroup α] [Small α] : Semigroup (Shrink α) 
goal: Semigroup (Shrink.{u_2, u_1} α)

full_name: instSemigroupWithZeroShrink
code: instance [SemigroupWithZero α] [Small α] : SemigroupWithZero (Shrink α) 
goal: SemigroupWithZero (Shrink.{u_2, u_1} α)

full_name: instAddCommSemigroupShrink
code: instance [AddCommSemigroup α] [Small α] : AddCommSemigroup (Shrink α) 
goal: AddCommSemigroup (Shrink.{u_2, u_1} α)

full_name: instCommSemigroupShrink
code: @[to_additive existing]
instance [CommSemigroup α] [Small α] : CommSemigroup (Shrink α) 
goal: CommSemigroup (Shrink.{u_2, u_1} α)

full_name: instMulZeroClassShrink
code: instance [MulZeroClass α] [Small α] : MulZeroClass (Shrink α) 
goal: MulZeroClass (Shrink.{u_2, u_1} α)

full_name: instAddZeroClassShrink
code: instance [AddZeroClass α] [Small α] : AddZeroClass (Shrink α) 
goal: AddZeroClass (Shrink.{u_2, u_1} α)

full_name: instMulOneClassShrink
code: @[to_additive existing]
instance [MulOneClass α] [Small α] : MulOneClass (Shrink α) 
goal: MulOneClass (Shrink.{u_2, u_1} α)

full_name: instMulZeroOneClassShrink
code: instance [MulZeroOneClass α] [Small α] : MulZeroOneClass (Shrink α) 
goal: MulZeroOneClass (Shrink.{u_2, u_1} α)

full_name: instAddMonoidShrink
code: instance [AddMonoid α] [Small α] : AddMonoid (Shrink α) 
goal: AddMonoid (Shrink.{u_2, u_1} α)

full_name: instMonoidShrink
code: @[to_additive existing]
instance [Monoid α] [Small α] : Monoid (Shrink α) 
goal: Monoid (Shrink.{u_2, u_1} α)

full_name: instAddCommMonoidShrink
code: instance [AddCommMonoid α] [Small α] : AddCommMonoid (Shrink α) 
goal: AddCommMonoid (Shrink.{u_2, u_1} α)

full_name: instCommMonoidShrink
code: @[to_additive existing]
instance [CommMonoid α] [Small α] : CommMonoid (Shrink α) 
goal: CommMonoid (Shrink.{u_2, u_1} α)

full_name: instAddGroupShrink
code: instance [AddGroup α] [Small α] : AddGroup (Shrink α) 
goal: AddGroup (Shrink.{u_2, u_1} α)

full_name: instGroupShrink
code: @[to_additive existing]
instance [Group α] [Small α] : Group (Shrink α) 
goal: Group (Shrink.{u_2, u_1} α)

full_name: instAddCommGroupShrink
code: instance [AddCommGroup α] [Small α] : AddCommGroup (Shrink α) 
goal: AddCommGroup (Shrink.{u_2, u_1} α)

full_name: instCommGroupShrink
code: @[to_additive existing]
instance [CommGroup α] [Small α] : CommGroup (Shrink α) 
goal: CommGroup (Shrink.{u_2, u_1} α)