abs_diff_lt_one_of_floor_eq_floor #693
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kbuzzard
reviewed
Feb 7, 2019
| @@ -5,7 +5,7 @@ Authors: Mario Carneiro | |||
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| Archimedean groups and fields. | |||
| -/ | |||
| import algebra.group_power data.rat | |||
| import algebra.group_power data.rat tactic.linarith | |||
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So I did not want to change the import graph when I was writing the theory of fractional parts a few days ago, because I was scared that linarith, or something it imported, might use this stuff, and I didn't really know how to check that it didn't.
This PR might conflict with mine, but only in a trivial way -- I think we might both have written new functions in about the same place.
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To check that the import did not break anything, I did the import, saved the file, and then I compiled the library. It went fine.
| @@ -67,6 +67,17 @@ eq_of_forall_le_iff $ λ a, by rw [le_floor, | |||
| theorem floor_sub_int (x : α) (z : ℤ) : ⌊x - z⌋ = ⌊x⌋ - z := | |||
| eq.trans (by rw [int.cast_neg]; refl) (floor_add_int _ _) | |||
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| lemma abs_diff_lt_one_of_floor_eq_floor {α : Type*} [decidable_linear_ordered_comm_ring α] [floor_ring α] | |||
| {x y : α} (h : floor x = floor y) : abs (x - y) < 1 := | |||
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Should be called abs_sub_lt_one_of_floor_eq_floor
cipher1024
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Feb 8, 2019
* abs_diff_lt_one_of_floor_eq_floor * better name
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