Commit 2021-09-07 01:49 d6a1fc02

feat(algebra/ordered_monoid): correct definition (#8877) Our definition of ordered_monoid is not the usual one, and this PR corrects that. The standard definition just says

(mul_le_mul_left       : ∀ a b : α, a ≤ b → ∀ c : α, c * a ≤ c * b)

while we currently have an extra axiom

(lt_of_add_lt_add_left : ∀ a b c : α, a + b < a + c → b < c)

(This was introduced in ancient times, https://github.com/leanprover-community/mathlib/commit/7d8e3f3a6de70da504406727dbe7697b2f7a62ee, with no indication of where the definition came from. I couldn't find it in other sources.) As @urkud pointed out a while ago on Zulip, these really are different. The second axiom does automatically hold for cancellative ordered monoids, however. This PR simply drops the axiom. In practice this causes no harm, because all the interesting examples are cancellative. There's a little bit of cleanup to do. In src/algebra/ordered_sub.lean four lemmas break, so I just added the necessary [contravariant_class _ _ (+) (<)] hypothesis. These lemmas aren't currently used in mathlib, but presumably where they are needed this typeclass will be available.