Ordered monoid structures on the order dual.

instance OrderDual.orderedCommMonoid {α : Type u} [OrderedCommMonoid α] : OrderedCommMonoid αᵒᵈ

Equations

• OrderDual.orderedCommMonoid = OrderedCommMonoid.mk ⋯

instance OrderDual.orderedAddCommMonoid {α : Type u} [OrderedAddCommMonoid α] : OrderedAddCommMonoid αᵒᵈ

Equations

• OrderDual.orderedAddCommMonoid = OrderedAddCommMonoid.mk ⋯

theorem OrderDual.OrderedCancelCommMonoid.to_mulLeftReflectLE {α : Type u} [OrderedCancelCommMonoid α] : MulLeftReflectLE αᵒᵈ

theorem OrderDual.OrderedCancelAddCommMonoid.to_mulLeftReflectLE {α : Type u} [OrderedCancelAddCommMonoid α] : AddLeftReflectLE αᵒᵈ

instance OrderDual.orderedCancelCommMonoid {α : Type u} [OrderedCancelCommMonoid α] : OrderedCancelCommMonoid αᵒᵈ

Equations

• OrderDual.orderedCancelCommMonoid = OrderedCancelCommMonoid.mk ⋯

instance OrderDual.orderedAddCancelCommMonoid {α : Type u} [OrderedCancelAddCommMonoid α] : OrderedCancelAddCommMonoid αᵒᵈ

Equations

• OrderDual.orderedAddCancelCommMonoid = OrderedCancelAddCommMonoid.mk ⋯

instance OrderDual.linearOrderedCancelCommMonoid {α : Type u} [LinearOrderedCancelCommMonoid α] : LinearOrderedCancelCommMonoid αᵒᵈ

Equations

• OrderDual.linearOrderedCancelCommMonoid = LinearOrderedCancelCommMonoid.mk ⋯ LinearOrder.decidableLE LinearOrder.decidableEq LinearOrder.decidableLT ⋯ ⋯ ⋯

instance OrderDual.linearOrderedAddCancelCommMonoid {α : Type u} [LinearOrderedCancelAddCommMonoid α] : LinearOrderedCancelAddCommMonoid αᵒᵈ

Equations

• OrderDual.linearOrderedAddCancelCommMonoid = LinearOrderedCancelAddCommMonoid.mk ⋯ LinearOrder.decidableLE LinearOrder.decidableEq LinearOrder.decidableLT ⋯ ⋯ ⋯

instance OrderDual.linearOrderedCommMonoid {α : Type u} [LinearOrderedCommMonoid α] : LinearOrderedCommMonoid αᵒᵈ

Equations

• OrderDual.linearOrderedCommMonoid = LinearOrderedCommMonoid.mk ⋯ LinearOrder.decidableLE LinearOrder.decidableEq LinearOrder.decidableLT ⋯ ⋯ ⋯

instance OrderDual.linearOrderedAddCommMonoid {α : Type u} [LinearOrderedAddCommMonoid α] : LinearOrderedAddCommMonoid αᵒᵈ

Equations

• OrderDual.linearOrderedAddCommMonoid = LinearOrderedAddCommMonoid.mk ⋯ LinearOrder.decidableLE LinearOrder.decidableEq LinearOrder.decidableLT ⋯ ⋯ ⋯