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

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Rob Lewis 2015-08-03 16:38:42 -04:00
parent 4dd4d7b3b8
commit 78942a0689
2 changed files with 4 additions and 2 deletions
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2
library/data/real/basic.lean
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@ -1096,6 +1096,8 @@ protected definition comm_ring [reducible] : algebra.comm_ring ℝ :=
apply mul_comm apply mul_comm
end end
open rat -- no coercions before
definition of_rat [coercion] (a : ℚ) : ℝ := quot.mk (s.r_const a) 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) := theorem of_rat_add (a b : ℚ) : of_rat a + of_rat b = of_rat (a + b) :=

4
library/data/real/complete.lean
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@ -452,7 +452,7 @@ theorem ex_smallest_of_bdd {P : ℤ → Prop} (Hbdd : ∃ b : ℤ, ∀ z : ℤ,
have Heltb : elt > b, begin have Heltb : elt > b, begin
apply int.lt_of_not_ge, apply int.lt_of_not_ge,
intro Hge, intro Hge,
apply false.elim ((Hb _ Hge) Helt) apply (Hb _ Hge) Helt
end, end,
have H' : P (b + of_nat (nat_abs (elt - b))), begin 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)), 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 have Heltb : elt < b, begin
apply int.lt_of_not_ge, apply int.lt_of_not_ge,
intro Hge, intro Hge,
apply false.elim ((Hb _ Hge) Helt) apply (Hb _ Hge) Helt
end, end,
have H' : P (b - of_nat (nat_abs (b - elt))), begin 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)), rewrite [of_nat_nat_abs_of_nonneg (int.le_of_lt (iff.mpr !int.sub_pos_iff_lt Heltb)),