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OrderDual.lean
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OrderDual.lean
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/-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura, Mario Carneiro, Johannes Hölzl
-/
import Mathlib.Algebra.Order.Group.Synonym
import Mathlib.Algebra.Order.Monoid.Unbundled.Defs
#align_import algebra.order.monoid.order_dual from "leanprover-community/mathlib"@"2258b40dacd2942571c8ce136215350c702dc78f"
/-! # Unbundled ordered monoid structures on the order dual. -/
universe u
variable {α : Type u}
open Function
namespace OrderDual
@[to_additive]
instance contravariantClass_mul_le [LE α] [Mul α] [c : ContravariantClass α α (· * ·) (· ≤ ·)] :
ContravariantClass αᵒᵈ αᵒᵈ (· * ·) (· ≤ ·) :=
⟨c.1.flip⟩
#align order_dual.contravariant_class_add_le OrderDual.contravariantClass_add_le
#align order_dual.contravariant_class_mul_le OrderDual.contravariantClass_mul_le
@[to_additive]
instance covariantClass_mul_le [LE α] [Mul α] [c : CovariantClass α α (· * ·) (· ≤ ·)] :
CovariantClass αᵒᵈ αᵒᵈ (· * ·) (· ≤ ·) :=
⟨c.1.flip⟩
#align order_dual.covariant_class_add_le OrderDual.covariantClass_add_le
#align order_dual.covariant_class_mul_le OrderDual.covariantClass_mul_le
@[to_additive]
instance contravariantClass_swap_mul_le [LE α] [Mul α]
[c : ContravariantClass α α (swap (· * ·)) (· ≤ ·)] :
ContravariantClass αᵒᵈ αᵒᵈ (swap (· * ·)) (· ≤ ·) :=
⟨c.1.flip⟩
#align order_dual.contravariant_class_swap_add_le OrderDual.contravariantClass_swap_add_le
#align order_dual.contravariant_class_swap_mul_le OrderDual.contravariantClass_swap_mul_le
@[to_additive]
instance covariantClass_swap_mul_le [LE α] [Mul α]
[c : CovariantClass α α (swap (· * ·)) (· ≤ ·)] :
CovariantClass αᵒᵈ αᵒᵈ (swap (· * ·)) (· ≤ ·) :=
⟨c.1.flip⟩
#align order_dual.covariant_class_swap_add_le OrderDual.covariantClass_swap_add_le
#align order_dual.covariant_class_swap_mul_le OrderDual.covariantClass_swap_mul_le
@[to_additive]
instance contravariantClass_mul_lt [LT α] [Mul α] [c : ContravariantClass α α (· * ·) (· < ·)] :
ContravariantClass αᵒᵈ αᵒᵈ (· * ·) (· < ·) :=
⟨c.1.flip⟩
#align order_dual.contravariant_class_add_lt OrderDual.contravariantClass_add_lt
#align order_dual.contravariant_class_mul_lt OrderDual.contravariantClass_mul_lt
@[to_additive]
instance covariantClass_mul_lt [LT α] [Mul α] [c : CovariantClass α α (· * ·) (· < ·)] :
CovariantClass αᵒᵈ αᵒᵈ (· * ·) (· < ·) :=
⟨c.1.flip⟩
#align order_dual.covariant_class_add_lt OrderDual.covariantClass_add_lt
#align order_dual.covariant_class_mul_lt OrderDual.covariantClass_mul_lt
@[to_additive]
instance contravariantClass_swap_mul_lt [LT α] [Mul α]
[c : ContravariantClass α α (swap (· * ·)) (· < ·)] :
ContravariantClass αᵒᵈ αᵒᵈ (swap (· * ·)) (· < ·) :=
⟨c.1.flip⟩
#align order_dual.contravariant_class_swap_add_lt OrderDual.contravariantClass_swap_add_lt
#align order_dual.contravariant_class_swap_mul_lt OrderDual.contravariantClass_swap_mul_lt
@[to_additive]
instance covariantClass_swap_mul_lt [LT α] [Mul α]
[c : CovariantClass α α (swap (· * ·)) (· < ·)] :
CovariantClass αᵒᵈ αᵒᵈ (swap (· * ·)) (· < ·) :=
⟨c.1.flip⟩
#align order_dual.covariant_class_swap_add_lt OrderDual.covariantClass_swap_add_lt
#align order_dual.covariant_class_swap_mul_lt OrderDual.covariantClass_swap_mul_lt