18 lines
462 B
Text
18 lines
462 B
Text
/-
|
||
Copyright (c) 2014 Floris van Doorn. All rights reserved.
|
||
Released under Apache 2.0 license as described in the file LICENSE.
|
||
|
||
Authors: Floris van Doorn, Jeremy Avigad
|
||
Subtraction on the natural numbers, as well as min, max, and distance.
|
||
-/
|
||
|
||
namespace nat
|
||
|
||
/- subtraction -/
|
||
|
||
-- defined in data/nat/sub.lean
|
||
protected theorem sub_le_sub_right {n m : ℕ} (H : n ≤ m) : Πk, n - k ≤ m - k
|
||
| 0 := H
|
||
| (succ z) := pred_le_pred (sub_le_sub_right z)
|
||
|
||
end nat
|