fix(library/data/rat/basic): define pow before migrate

library/data/rat/basic.lean

@@ -512,12 +512,17 @@ section migrate_algebra
     has_decidable_eq := has_decidable_eq⦄
 
   local attribute rat.discrete_field [instance]
+
   definition divide (a b : rat) := algebra.divide a b
-  infix `/` := divide
+  infix [priority rat.prio] `/` := divide
+
   definition dvd (a b : rat) := algebra.dvd a b
 
+  definition pow (a : ℚ) (n : ℕ) : ℚ := algebra.pow a n
+  infix [priority rat.prio] ^ := pow
+
   migrate from algebra with rat
-    replacing sub → rat.sub, divide → divide, dvd → dvd
+    replacing sub → rat.sub, divide → divide, dvd → dvd, pow → pow
 
 end migrate_algebra
 
@@ -537,5 +542,4 @@ decidable.by_cases
           by rewrite [Hc, !int.mul_div_cancel_left bnz, mul.comm]),
     iff.mpr (eq_div_iff_mul_eq bnz') H')
 
-
 end rat

library/data/real/complete.lean

@@ -20,13 +20,11 @@ open -[coercions] nat
 open eq.ops
 open pnat
 
-
 local notation 2 := subtype.tag (nat.of_num 2) dec_trivial
 local notation 3 := subtype.tag (nat.of_num 3) dec_trivial
 
 namespace s
 
-
 theorem rat_approx_l1 {s : seq} (H : regular s) :
         ∀ n : ℕ+, ∃ q : ℚ, ∃ N : ℕ+, ∀ m : ℕ+, m ≥ N → abs (s m - q) ≤ n⁻¹ :=
   begin
@@ -749,9 +747,6 @@ theorem over_succ (n : ℕ) : over_seq (succ n) =
     apply H
   end
 
--- ???
-theorem rat.pow_add (a : ℚ) (m : ℕ) : ∀ n, rat.pow a (m + n) = rat.pow a m * rat.pow a n := rat.pow_add a m
-
 theorem width (n : ℕ) : over_seq n - under_seq n = (over - under) / (rat.pow 2 n) :=
   nat.induction_on n
     (by xrewrite [over_0, under_0, rat.pow_zero, rat.div_one])