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[Merged by Bors] - feat: Monovariance under algebraic operations #7648

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[Merged by Bors] - feat: Monovariance under algebraic operations #7648

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7c1f469
feat: Basic lemmas about positivity of `a • b`
YaelDillies Oct 12, 2023
eeef6a2
whoops
YaelDillies Oct 12, 2023
58ca76f
feat: Monovariance under algebraic operations
YaelDillies Oct 12, 2023
f2f6aa2
style
YaelDillies Oct 12, 2023
37b4582
Merge remote-tracking branch 'origin/master' into algebra_monovary
YaelDillies Oct 30, 2023
fe148d7
update Mathlib
YaelDillies Oct 30, 2023
ee06c57
use mul
YaelDillies Nov 14, 2023
ce50dd0
bleh
YaelDillies Nov 15, 2023
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1 change: 1 addition & 0 deletions Mathlib.lean
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Expand Up @@ -377,6 +377,7 @@ import Mathlib.Algebra.Order.Monoid.Units
import Mathlib.Algebra.Order.Monoid.WithTop
import Mathlib.Algebra.Order.Monoid.WithZero.Basic
import Mathlib.Algebra.Order.Monoid.WithZero.Defs
import Mathlib.Algebra.Order.Monovary
import Mathlib.Algebra.Order.Nonneg.Field
import Mathlib.Algebra.Order.Nonneg.Floor
import Mathlib.Algebra.Order.Nonneg.Module
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7 changes: 7 additions & 0 deletions Mathlib/Algebra/Order/Group/Defs.lean
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Expand Up @@ -1018,6 +1018,13 @@ theorem div_lt_div'' (hab : a < b) (hcd : c < d) : a / d < b / c := by

end Preorder

section LinearOrder
variable [LinearOrder α] [CovariantClass α α (· * ·) (· ≤ ·)] {a b c d : α}

@[to_additive] lemma lt_or_lt_of_div_lt_div : a / d < b / c → a < b ∨ c < d := by
contrapose!; exact fun h ↦ div_le_div'' h.1 h.2

end LinearOrder
end CommGroup

section LinearOrder
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