fix(library/data/real): fix num -> rat -> real coercion chain

library/data/real/basic.lean

@@ -1096,6 +1096,8 @@ protected definition comm_ring [reducible] : algebra.comm_ring ℝ :=
     apply mul_comm
   end
 
+open rat -- no coercions before
+
 definition of_rat [coercion] (a : ℚ) : ℝ := quot.mk (s.r_const a)
 
 theorem of_rat_add (a b : ℚ) : of_rat a + of_rat b = of_rat (a + b) :=

library/data/real/complete.lean

@@ -452,7 +452,7 @@ theorem ex_smallest_of_bdd {P : ℤ → Prop} (Hbdd : ∃ b : ℤ, ∀ z : ℤ,
     have Heltb : elt > b, begin
       apply int.lt_of_not_ge,
       intro Hge,
-      apply false.elim ((Hb _ Hge) Helt)
+      apply (Hb _ Hge) Helt
     end,
     have H' : P (b + of_nat (nat_abs (elt - b))), begin
       rewrite [of_nat_nat_abs_of_nonneg (int.le_of_lt (iff.mpr !int.sub_pos_iff_lt Heltb)),
@@ -489,7 +489,7 @@ theorem ex_largest_of_bdd {P : ℤ → Prop} (Hbdd : ∃ b : ℤ, ∀ z : ℤ, z
     have Heltb : elt < b, begin
       apply int.lt_of_not_ge,
       intro Hge,
-      apply false.elim ((Hb _ Hge) Helt)
+      apply (Hb _ Hge) Helt
     end,
     have H' : P (b - of_nat (nat_abs (b - elt))), begin
       rewrite [of_nat_nat_abs_of_nonneg (int.le_of_lt (iff.mpr !int.sub_pos_iff_lt Heltb)),