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

full_name: Prod.instOrderedCommMonoid
code: @[to_additive]
instance [OrderedCommMonoid α] [OrderedCommMonoid β] : OrderedCommMonoid (α × β) 
goal: OrderedCommMonoid (α × β)

full_name: Prod.instOrderedAddCommMonoid
code: @[to_additive]
instance [OrderedCommMonoid α] [OrderedCommMonoid β] : OrderedCommMonoid (α × β) 
goal: OrderedAddCommMonoid (α × β)

full_name: Prod.instOrderedAddCancelCommMonoid
code: @[to_additive]
instance instOrderedCancelCommMonoid [OrderedCancelCommMonoid α] [OrderedCancelCommMonoid β] :
    OrderedCancelCommMonoid (α × β) 
goal: OrderedCancelAddCommMonoid (α × β)

full_name: Prod.instOrderedCancelCommMonoid
code: @[to_additive]
instance instOrderedCancelCommMonoid [OrderedCancelCommMonoid α] [OrderedCancelCommMonoid β] :
    OrderedCancelCommMonoid (α × β) 
goal: OrderedCancelCommMonoid (α × β)

full_name: Prod.instExistsAddOfLE
code: @[to_additive]
instance [LE α] [LE β] [Mul α] [Mul β] [ExistsMulOfLE α] [ExistsMulOfLE β] :
    ExistsMulOfLE (α × β) 
goal: ExistsAddOfLE (α × β)

full_name: Prod.instExistsMulOfLE
code: @[to_additive]
instance [LE α] [LE β] [Mul α] [Mul β] [ExistsMulOfLE α] [ExistsMulOfLE β] :
    ExistsMulOfLE (α × β) 
goal: ExistsMulOfLE (α × β)

full_name: Prod.instCanonicallyOrderedCommMonoid
code: @[to_additive]
instance [CanonicallyOrderedCommMonoid α] [CanonicallyOrderedCommMonoid β] :
    CanonicallyOrderedCommMonoid (α × β) 
goal: CanonicallyOrderedCommMonoid (α × β)

full_name: Prod.instCanonicallyOrderedAddCommMonoid
code: @[to_additive]
instance [CanonicallyOrderedCommMonoid α] [CanonicallyOrderedCommMonoid β] :
    CanonicallyOrderedCommMonoid (α × β) 
goal: CanonicallyOrderedAddCommMonoid (α × β)

full_name: Prod.Lex.orderedAddCommMonoid
code: @[to_additive]
instance orderedCommMonoid [OrderedCommMonoid α]
    [CovariantClass α α (· * ·) (· < ·)] [OrderedCommMonoid β] :
    OrderedCommMonoid (α ×ₗ β) 
goal: OrderedAddCommMonoid (Lex (α × β))

full_name: Prod.Lex.orderedCommMonoid
code: @[to_additive]
instance orderedCommMonoid [OrderedCommMonoid α]
    [CovariantClass α α (· * ·) (· < ·)] [OrderedCommMonoid β] :
    OrderedCommMonoid (α ×ₗ β) 
goal: OrderedCommMonoid (Lex (α × β))

full_name: Prod.Lex.orderedCancelCommMonoid
code: @[to_additive]
instance orderedCancelCommMonoid [OrderedCancelCommMonoid α] [OrderedCancelCommMonoid β] :
    OrderedCancelCommMonoid (α ×ₗ β) 
goal: OrderedCancelCommMonoid (Lex (α × β))

full_name: Prod.Lex.orderedAddCancelCommMonoid
code: @[to_additive]
instance orderedCancelCommMonoid [OrderedCancelCommMonoid α] [OrderedCancelCommMonoid β] :
    OrderedCancelCommMonoid (α ×ₗ β) 
goal: OrderedCancelAddCommMonoid (Lex (α × β))

full_name: Prod.Lex.linearOrderedCancelCommMonoid
code: @[to_additive]
instance linearOrderedCancelCommMonoid [LinearOrderedCancelCommMonoid α]
    [LinearOrderedCancelCommMonoid β] : LinearOrderedCancelCommMonoid (α ×ₗ β) 
goal: LinearOrderedCancelCommMonoid (Lex (α × β))

full_name: Prod.Lex.linearOrderedAddCancelCommMonoid
code: @[to_additive]
instance linearOrderedCancelCommMonoid [LinearOrderedCancelCommMonoid α]
    [LinearOrderedCancelCommMonoid β] : LinearOrderedCancelCommMonoid (α ×ₗ β) 
goal: LinearOrderedCancelAddCommMonoid (Lex (α × β))