File: Mathlib/Algebra/Order/Monoid/TypeTags.lean

full_name: instLEMultiplicative
code: instance : ∀ [LE α], LE (Multiplicative α) 
goal: LE (Multiplicative α)

full_name: instLEAdditive
code: instance : ∀ [LE α], LE (Additive α) 
goal: LE (Additive α)

full_name: instLTMultiplicative
code: instance : ∀ [LT α], LT (Multiplicative α) 
goal: LT (Multiplicative α)

full_name: instLTAdditive
code: instance : ∀ [LT α], LT (Additive α) 
goal: LT (Additive α)

full_name: Multiplicative.preorder
code: instance Multiplicative.preorder : ∀ [Preorder α], Preorder (Multiplicative α) 
goal: Preorder (Multiplicative α)

full_name: Additive.preorder
code: instance Additive.preorder : ∀ [Preorder α], Preorder (Additive α) 
goal: Preorder (Additive α)

full_name: Multiplicative.partialOrder
code: instance Multiplicative.partialOrder : ∀ [PartialOrder α], PartialOrder (Multiplicative α) 
goal: PartialOrder (Multiplicative α)

full_name: Additive.partialOrder
code: instance Additive.partialOrder : ∀ [PartialOrder α], PartialOrder (Additive α) 
goal: PartialOrder (Additive α)

full_name: Multiplicative.linearOrder
code: instance Multiplicative.linearOrder : ∀ [LinearOrder α], LinearOrder (Multiplicative α) 
goal: LinearOrder (Multiplicative α)

full_name: Additive.linearOrder
code: instance Additive.linearOrder : ∀ [LinearOrder α], LinearOrder (Additive α) 
goal: LinearOrder (Additive α)

full_name: Multiplicative.orderBot
code: instance Multiplicative.orderBot [LE α] : ∀ [OrderBot α], OrderBot (Multiplicative α) 
goal: OrderBot (Multiplicative α)

full_name: Additive.orderBot
code: instance Additive.orderBot [LE α] : ∀ [OrderBot α], OrderBot (Additive α) 
goal: OrderBot (Additive α)

full_name: Multiplicative.orderTop
code: instance Multiplicative.orderTop [LE α] : ∀ [OrderTop α], OrderTop (Multiplicative α) 
goal: OrderTop (Multiplicative α)

full_name: Additive.orderTop
code: instance Additive.orderTop [LE α] : ∀ [OrderTop α], OrderTop (Additive α) 
goal: OrderTop (Additive α)

full_name: Multiplicative.boundedOrder
code: instance Multiplicative.boundedOrder [LE α] : ∀ [BoundedOrder α], BoundedOrder (Multiplicative α) 
goal: BoundedOrder (Multiplicative α)

full_name: Additive.boundedOrder
code: instance Additive.boundedOrder [LE α] : ∀ [BoundedOrder α], BoundedOrder (Additive α) 
goal: BoundedOrder (Additive α)

full_name: Multiplicative.orderedCommMonoid
code: instance Multiplicative.orderedCommMonoid [OrderedAddCommMonoid α] :
    OrderedCommMonoid (Multiplicative α) 
goal: OrderedCommMonoid (Multiplicative α)

full_name: Additive.orderedAddCommMonoid
code: instance Additive.orderedAddCommMonoid [OrderedCommMonoid α] :
    OrderedAddCommMonoid (Additive α) 
goal: OrderedAddCommMonoid (Additive α)

full_name: Multiplicative.orderedCancelAddCommMonoid
code: instance Multiplicative.orderedCancelAddCommMonoid [OrderedCancelAddCommMonoid α] :
    OrderedCancelCommMonoid (Multiplicative α) 
goal: OrderedCancelCommMonoid (Multiplicative α)

full_name: Additive.orderedCancelAddCommMonoid
code: instance Additive.orderedCancelAddCommMonoid [OrderedCancelCommMonoid α] :
    OrderedCancelAddCommMonoid (Additive α) 
goal: OrderedCancelAddCommMonoid (Additive α)

full_name: Multiplicative.linearOrderedCommMonoid
code: instance Multiplicative.linearOrderedCommMonoid [LinearOrderedAddCommMonoid α] :
    LinearOrderedCommMonoid (Multiplicative α) 
goal: LinearOrderedCommMonoid (Multiplicative α)

full_name: Additive.linearOrderedAddCommMonoid
code: instance Additive.linearOrderedAddCommMonoid [LinearOrderedCommMonoid α] :
    LinearOrderedAddCommMonoid (Additive α) 
goal: LinearOrderedAddCommMonoid (Additive α)

full_name: Multiplicative.existsMulOfLe
code: instance Multiplicative.existsMulOfLe [Add α] [LE α] [ExistsAddOfLE α] :
    ExistsMulOfLE (Multiplicative α) 
goal: ExistsMulOfLE (Multiplicative α)

full_name: Additive.existsAddOfLe
code: instance Additive.existsAddOfLe [Mul α] [LE α] [ExistsMulOfLE α] : ExistsAddOfLE (Additive α) 
goal: ExistsAddOfLE (Additive α)

full_name: Multiplicative.canonicallyOrderedCommMonoid
code: instance Multiplicative.canonicallyOrderedCommMonoid [CanonicallyOrderedAddCommMonoid α] :
    CanonicallyOrderedCommMonoid (Multiplicative α) 
goal: CanonicallyOrderedCommMonoid (Multiplicative α)

full_name: Additive.canonicallyOrderedAddCommMonoid
code: instance Additive.canonicallyOrderedAddCommMonoid [CanonicallyOrderedCommMonoid α] :
    CanonicallyOrderedAddCommMonoid (Additive α) 
goal: CanonicallyOrderedAddCommMonoid (Additive α)

full_name: Multiplicative.canonicallyLinearOrderedCommMonoid
code: instance Multiplicative.canonicallyLinearOrderedCommMonoid
    [CanonicallyLinearOrderedAddCommMonoid α] :
    CanonicallyLinearOrderedCommMonoid (Multiplicative α) 
goal: CanonicallyLinearOrderedCommMonoid (Multiplicative α)

full_name: instCanonicallyLinearOrderedAddCommMonoidAdditiveOfCanonicallyLinearOrderedCommMonoid
code: instance [CanonicallyLinearOrderedCommMonoid α] :
    CanonicallyLinearOrderedAddCommMonoid (Additive α) 
goal: CanonicallyLinearOrderedAddCommMonoid (Additive α)

full_name: Additive.ofMul_le
code: @[simp]
theorem ofMul_le {a b : α} : ofMul a ≤ ofMul b ↔ a ≤ b 
goal: Additive.ofMul a ≤ Additive.ofMul b ↔ a ≤ b

full_name: Additive.ofMul_lt
code: @[simp]
theorem ofMul_lt {a b : α} : ofMul a < ofMul b ↔ a < b 
goal: Additive.ofMul a < Additive.ofMul b ↔ a < b

full_name: Additive.toMul_le
code: @[simp]
theorem toMul_le {a b : Additive α} : toMul a ≤ toMul b ↔ a ≤ b 
goal: Additive.toMul a ≤ Additive.toMul b ↔ a ≤ b

full_name: Additive.toMul_lt
code: @[simp]
theorem toMul_lt {a b : Additive α} : toMul a < toMul b ↔ a < b 
goal: Additive.toMul a < Additive.toMul b ↔ a < b

full_name: Multiplicative.ofAdd_le
code: @[simp]
theorem ofAdd_le {a b : α} : ofAdd a ≤ ofAdd b ↔ a ≤ b 
goal: Multiplicative.ofAdd a ≤ Multiplicative.ofAdd b ↔ a ≤ b

full_name: Multiplicative.ofAdd_lt
code: @[simp]
theorem ofAdd_lt {a b : α} : ofAdd a < ofAdd b ↔ a < b 
goal: Multiplicative.ofAdd a < Multiplicative.ofAdd b ↔ a < b

full_name: Multiplicative.toAdd_le
code: @[simp]
theorem toAdd_le {a b : Multiplicative α} : toAdd a ≤ toAdd b ↔ a ≤ b 
goal: Multiplicative.toAdd a ≤ Multiplicative.toAdd b ↔ a ≤ b

full_name: Multiplicative.toAdd_lt
code: @[simp]
theorem toAdd_lt {a b : Multiplicative α} : toAdd a < toAdd b ↔ a < b 
goal: Multiplicative.toAdd a < Multiplicative.toAdd b ↔ a < b