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feat(library/init/ordered_ring): add linear_ordered_ring

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Leonardo de Moura 2016-11-24 14:34:49 -08:00
parent baed136148
commit 4d36effe85
1 changed files with 17 additions and 0 deletions
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17
library/init/ordered_ring.lean
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@ -128,3 +128,20 @@ instance ordered_ring.to_ordered_semiring [s : ordered_ring α] : ordered_semiri
mul_lt_mul_of_pos_left := @ordered_ring.mul_lt_mul_of_pos_left α _,
mul_lt_mul_of_pos_right := @ordered_ring.mul_lt_mul_of_pos_right α _,
lt_of_add_lt_add_left := @lt_of_add_lt_add_left α _}
class linear_ordered_ring (α : Type u) extends ordered_ring α, linear_strong_order_pair α :=
(zero_lt_one : lt zero one)
instance linear_ordered_ring.to_linear_ordered_semiring [s : linear_ordered_ring α] : linear_ordered_semiring α :=
{ s with
mul_zero := mul_zero,
zero_mul := zero_mul,
add_left_cancel := @add_left_cancel α _,
add_right_cancel := @add_right_cancel α _,
le_of_add_le_add_left := @le_of_add_le_add_left α _,
mul_le_mul_of_nonneg_left := @mul_le_mul_of_nonneg_left α _,
mul_le_mul_of_nonneg_right := @mul_le_mul_of_nonneg_right α _,
mul_lt_mul_of_pos_left := @mul_lt_mul_of_pos_left α _,
mul_lt_mul_of_pos_right := @mul_lt_mul_of_pos_right α _,
le_total := linear_ordered_ring.le_total,
lt_of_add_lt_add_left := @lt_of_add_lt_add_left α _ }