α : Type u_1
inst✝³ : AddGroup α
inst✝² : LinearOrder α
inst✝¹ : CovariantClass α α (fun x x_1 => x + x_1) fun x x_1 => x ≤ x_1
a b c : α
inst✝ : CovariantClass α α (swap fun x x_1 => x + x_1) fun x x_1 => x ≤ x_1
ha : a ≤ 0
hab : b ≤ a
⊢ -a ≤ -b
α : Type u_1
inst✝³ : AddGroup α
inst✝² : LinearOrder α
inst✝¹ : CovariantClass α α (fun x x_1 => x + x_1) fun x x_1 => x ≤ x_1
a b c : α
inst✝ : CovariantClass α α (swap fun x x_1 => x + x_1) fun x x_1 => x ≤ x_1
ha : a ≤ 0
hab : b ≤ a
⊢ abs a ≤ abs b
rw [abs_of_nonpos ha, abs_of_nonpos (hab.trans ha)]
no goals
α : Type u_1
inst✝³ : AddGroup α
inst✝² : LinearOrder α
inst✝¹ : CovariantClass α α (fun x x_1 => x + x_1) fun x x_1 => x ≤ x_1
a b c : α
inst✝ : CovariantClass α α (swap fun x x_1 => x + x_1) fun x x_1 => x ≤ x_1
ha : a ≤ 0
hab : b ≤ a
⊢ -a ≤ -b
exact neg_le_neg_iff.mpr hab