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[Merged by Bors] - feat: a * b ≤ c * d → min a b ≤ max c d #967

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[Merged by Bors] - feat: a * b ≤ c * d → min a b ≤ max c d #967

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10 changes: 10 additions & 0 deletions Mathlib/Algebra/Order/Monoid/Lemmas.lean
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Expand Up @@ -6,6 +6,8 @@ Yuyang Zhao
-/
import Mathlib.Algebra.CovariantAndContravariant
import Mathlib.Init.Data.Ordering.Basic
import Mathlib.Order.MinMax
import Mathlib.Tactic.Contrapose
import Mathlib.Tactic.PushNeg
import Mathlib.Tactic.Use

Expand Down Expand Up @@ -249,6 +251,14 @@ theorem mul_right_cancel'' [ContravariantClass α α (swap (· * ·)) (· ≤ ·

end PartialOrder

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

@[to_additive] lemma min_le_max_of_mul_le_mul (h : a * b ≤ c * d) : min a b ≤ max c d :=
by simp_rw [min_le_iff, le_max_iff]; contrapose! h; exact mul_lt_mul_of_lt_of_lt h.1.1 h.2.2
Comment on lines +258 to +259
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I think the style in mathlib4 is that the by goes on the line before, like this:

@[to_additive] lemma min_le_max_of_mul_le_mul (h : a * b ≤ c * d) : min a b ≤ max c d := by 
  simp_rw [min_le_iff, le_max_iff]; contrapose! h; exact mul_lt_mul_of_lt_of_lt h.1.1 h.2.2

But other than that this looks fine.

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Whoops, sorry.


end LinearOrder
end Mul

-- using one
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