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chore: add Nat.add_mul and Nat.mul_add for tutorial

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Leonardo de Moura 2021-08-25 06:44:12 -07:00
parent fb41e0f4e5
commit f08b542068
1 changed files with 6 additions and 0 deletions
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6
src/Init/Data/Nat/Basic.lean
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@ -126,6 +126,12 @@ protected theorem right_distrib (n m k : Nat) : (n + m) * k = n * k + m * k :=
have h₄ : n * k + k * m = n * k + m * k := Nat.mul_comm m k ▸ rfl
((h₁.trans h₂).trans h₃).trans h₄
protected theorem mul_add (n m k : Nat) : n * (m + k) = n * m + n * k :=
Nat.left_distrib n m k
protected theorem add_mul (n m k : Nat) : (n + m) * k = n * k + m * k :=
Nat.right_distrib n m k
protected theorem mul_assoc : ∀ (n m k : Nat), (n * m) * k = n * (m * k)
| n, m, 0 => rfl
| n, m, succ k =>