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port data/nat/gcd.lean (except for pow_dvd_pow_iff) #20

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merged 10 commits into from
Jul 2, 2021
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port data/nat/gcd.lean (except for pow_dvd_pow_iff) #20

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0a95387
port data/nat/gcd.lean (except for pow_dvd_pow_iff)
dwrensha Jun 21, 2021
aa74241
minor touchup
dwrensha Jun 21, 2021
7d0edf9
move Dvd class and notation to top level file, like Mem
dwrensha Jun 21, 2021
831c412
add copyright header
dwrensha Jun 21, 2021
752acd5
add missing imports
dwrensha Jun 22, 2021
c787003
gcd_induction -> gcd.induction
dwrensha Jun 23, 2021
b2ab22b
simplify usages of gcd.induction via the 'induction' tactic
dwrensha Jun 23, 2021
5ef8f93
remove unused import
dwrensha Jun 23, 2021
fd1c568
tiny simplification of gcd_rec proof
dwrensha Jul 1, 2021
8b65f85
use eq_zero_of_mul_eq_zero
dwrensha Jul 1, 2021
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2 changes: 2 additions & 0 deletions Mathlib.lean
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Expand Up @@ -9,7 +9,9 @@ import Mathlib.Data.Equiv.Basic
import Mathlib.Data.Equiv.Functor
import Mathlib.Data.List.Basic
import Mathlib.Data.Nat.Basic
import Mathlib.Data.Nat.Gcd
import Mathlib.Data.UInt
import Mathlib.Dvd
import Mathlib.Function
import Mathlib.Logic.Basic
import Mathlib.Logic.Function.Basic
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4 changes: 4 additions & 0 deletions Mathlib/Data/Nat/Basic.lean
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Expand Up @@ -157,6 +157,10 @@ lemma eq_of_mul_eq_mul_left {m k n : ℕ} (Hn : 0 < n) (H : n * m = n * k) : m =
Nat.le_antisymm (Nat.le_of_mul_le_mul_left (Nat.le_of_eq H) Hn)
(Nat.le_of_mul_le_mul_left (Nat.le_of_eq H.symm) Hn)

lemma eq_of_mul_eq_mul_right {n m k : ℕ} (Hm : 0 < m) (H : n * m = k * m) : n = k :=
by rw [Nat.mul_comm n m, Nat.mul_comm k m] at H
exact Nat.eq_of_mul_eq_mul_left Hm H

protected lemma add_self_ne_one : ∀ (n : ℕ), n + n ≠ 1
| n+1, h =>
have h1 : succ (succ (n + n)) = 1 := succ_add n n ▸ h
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