[Merged by Bors] - feat(order/monotone): add lemmas about cmp
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urkud
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Jun 12, 2022
| @@ -543,9 +543,10 @@ theorem dual_insert [preorder α] [is_total α (≤)] [@decidable_rel α (≤)] | |||
| ∀ t : ordnode α, dual (ordnode.insert x t) = @ordnode.insert αᵒᵈ _ _ x (dual t) | |||
| | nil := rfl | |||
| | (node _ l y r) := begin | |||
| rw [ordnode.insert, dual, ordnode.insert, order_dual.cmp_le_flip, ← cmp_le_swap x y], | |||
| have : @cmp_le αᵒᵈ _ _ x y = cmp_le y x := rfl, | |||
| rw [ordnode.insert, dual, ordnode.insert, this, ← cmp_le_swap x y], | |||
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IMHO, we should use order_dual in definitions and lemmas about ordnode.dual but I don't want to do this refactor myself (also, I don't want to to any refactor there without Mario's approval).
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Also replace
order_dual.cmp_le_flipwith lemmas aboutto_dualandof_dual.