diff --git a/library/data/nat/basic.lean b/library/data/nat/basic.lean index 40924c761..6364c0fcb 100644 --- a/library/data/nat/basic.lean +++ b/library/data/nat/basic.lean @@ -126,7 +126,7 @@ nat.induction_on m theorem add.comm [simp] (n m : ℕ) : n + m = m + n := nat.induction_on m - (!add_zero ⬝ !zero_add⁻¹) + (by rewrite [add_zero, zero_add]) (take k IH, calc n + succ k = succ (n+k) : add_succ ... = succ (k + n) : IH @@ -137,7 +137,7 @@ theorem succ_add_eq_succ_add (n m : ℕ) : succ n + m = n + succ m := theorem add.assoc [simp] (n m k : ℕ) : (n + m) + k = n + (m + k) := nat.induction_on k - (!add_zero ▸ !add_zero) + (by rewrite +add_zero) (take l IH, calc (n + m) + succ l = succ ((n + m) + l) : add_succ