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refactor(library/data/nat/basic): remove unnecessary nat_

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Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
This commit is contained in:
Leonardo de Moura 2014-09-03 16:14:29 -07:00
parent e51c4ad2e9
commit 7500761114
1 changed files with 2 additions and 2 deletions

4
library/data/nat/basic.lean
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@ -24,9 +24,9 @@ inductive nat : Type :=
notation `ℕ` := nat
theorem nat_rec_zero {P : ℕ → Type} (x : P zero) (f : ∀m, P m → P (succ m)) : nat_rec x f zero = x
theorem rec_zero {P : ℕ → Type} (x : P zero) (f : ∀m, P m → P (succ m)) : nat_rec x f zero = x
theorem nat_rec_succ {P : ℕ → Type} (x : P zero) (f : ∀m, P m → P (succ m)) (n : ℕ) :
theorem rec_succ {P : ℕ → Type} (x : P zero) (f : ∀m, P m → P (succ m)) (n : ℕ) :
nat_rec x f (succ n) = f n (nat_rec x f n)
theorem induction_on [protected] {P : ℕ → Prop} (a : ℕ) (H1 : P zero) (H2 : ∀ (n : ℕ) (IH : P n), P (succ n)) :