diff --git a/library/algebra/ordered_group.lean b/library/algebra/ordered_group.lean index 644e4fe485..f2f792b14d 100644 --- a/library/algebra/ordered_group.lean +++ b/library/algebra/ordered_group.lean @@ -201,17 +201,17 @@ structure ordered_comm_group [class] (A : Type) extends add_comm_group A, order_ definition ordered_comm_group.to_ordered_cancel_comm_monoid [instance] [coercion] [s : ordered_comm_group A] : ordered_cancel_comm_monoid A := -ordered_cancel_comm_monoid.mk ordered_comm_group.add ordered_comm_group.add_assoc - (@ordered_comm_group.zero A s) zero_add add_zero ordered_comm_group.add_comm - (@add.left_cancel _ _) (@add.right_cancel _ _) - has_le.le le.refl (@le.trans _ _) (@le.antisymm _ _) - has_lt.lt (@lt_iff_le_and_ne _ _) ordered_comm_group.add_le_add_left -proof - take a b c : A, - assume H : a + b ≤ a + c, - have H' : -a + (a + b) ≤ -a + (a + c), from ordered_comm_group.add_le_add_left _ _ H _, - !neg_add_cancel_left ▸ !neg_add_cancel_left ▸ H' -qed +⦃ ordered_cancel_comm_monoid, + add_left_cancel := @add.left_cancel _ _, + add_right_cancel := @add.right_cancel _ _, + le_of_add_le_add_left := + proof + take a b c : A, + assume H : a + b ≤ a + c, + have H' : -a + (a + b) ≤ -a + (a + c), from ordered_comm_group.add_le_add_left _ _ H _, + !neg_add_cancel_left ▸ !neg_add_cancel_left ▸ H' + qed, + using s ⦄ section variables [s : ordered_comm_group A] (a b c d e : A)