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feat(order): add lemma (#1375)
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fpvandoorn authored and mergify[bot] committed Sep 4, 2019
1 parent 5d59e8b commit 06cffeb
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3 changes: 3 additions & 0 deletions src/algebra/order.lean
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Expand Up @@ -164,6 +164,9 @@ lemma le_iff_le_iff_lt_iff_lt {β} [decidable_linear_order α] [decidable_linear
{a b : α} {c d : β} : (a ≤ b ↔ c ≤ d) ↔ (b < a ↔ d < c) :=
⟨lt_iff_lt_of_le_iff_le, λ H, not_lt.symm.trans $ iff.trans (not_congr H) $ not_lt⟩

lemma min_le_max [decidable_linear_order α] (a b : α) : min a b ≤ max a b :=
le_trans (min_le_left a b) (le_max_left a b)

end decidable

namespace ordering
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