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docs(algebra/order/floor): Update floor_semiring docs to reflect it's…
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… just an ordered_semiring (#12756)

The docs say that `floor_semiring` is a linear ordered semiring, but it is only an `ordered_semiring` in the code. Change the docs to reflect this fact.
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khwilson committed Mar 17, 2022
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Showing 1 changed file with 4 additions and 3 deletions.
7 changes: 4 additions & 3 deletions src/algebra/order/floor.lean
Expand Up @@ -15,7 +15,7 @@ We define the natural- and integer-valued floor and ceil functions on linearly o
## Main Definitions
* `floor_semiring`: A linearly ordered semiring with natural-valued floor and ceil.
* `floor_semiring`: An ordered semiring with natural-valued floor and ceil.
* `nat.floor a`: Greatest natural `n` such that `n ≤ a`. Equal to `0` if `a < 0`.
* `nat.ceil a`: Least natural `n` such that `a ≤ n`.
Expand Down Expand Up @@ -51,8 +51,9 @@ variables {α : Type*}

/-! ### Floor semiring -/

/-- A `floor_semiring` is a linear ordered semiring over `α` with a function
`floor : α → ℕ` satisfying `∀ (n : ℕ) (x : α), n ≤ ⌊x⌋ ↔ (n : α) ≤ x)`. -/
/-- A `floor_semiring` is an ordered semiring over `α` with a function
`floor : α → ℕ` satisfying `∀ (n : ℕ) (x : α), n ≤ ⌊x⌋ ↔ (n : α) ≤ x)`.
Note that many lemmas require a `linear_order`. Please see the above `TODO`. -/
class floor_semiring (α) [ordered_semiring α] :=
(floor : α → ℕ)
(ceil : α → ℕ)
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