--- a/src/HOL/Real/RealArith.thy Thu Feb 05 10:45:28 2004 +0100
+++ b/src/HOL/Real/RealArith.thy Tue Feb 10 12:02:11 2004 +0100
@@ -62,13 +62,13 @@
lemma eq_real_number_of [simp]:
"((number_of v :: real) = number_of v') =
- iszero (number_of (bin_add v (bin_minus v')))"
+ iszero (number_of (bin_add v (bin_minus v')) :: int)"
by (simp only: real_number_of_def real_of_int_inject eq_number_of_eq)
text{*@{term neg} is used in rewrite rules for binary comparisons*}
lemma less_real_number_of [simp]:
"((number_of v :: real) < number_of v') =
- neg (number_of (bin_add v (bin_minus v')))"
+ neg (number_of (bin_add v (bin_minus v')) :: int)"
by (simp only: real_number_of_def real_of_int_less_iff less_number_of_eq_neg)
@@ -134,12 +134,12 @@
have. *}
lemma real_of_nat_number_of [simp]:
"real (number_of v :: nat) =
- (if neg (number_of v) then 0
+ (if neg (number_of v :: int) then 0
else (number_of v :: real))"
proof cases
- assume "neg (number_of v)" thus ?thesis by simp
+ assume "neg (number_of v :: int)" thus ?thesis by simp
next
- assume neg: "~ neg (number_of v)"
+ assume neg: "~ neg (number_of v :: int)"
thus ?thesis
by (simp only: nat_number_of_def real_of_nat_real_of_int [OF neg], simp)
qed
@@ -222,7 +222,7 @@
lemma abs_nat_number_of [simp]:
"abs (number_of v :: real) =
- (if neg (number_of v) then number_of (bin_minus v)
+ (if neg (number_of v :: int) then number_of (bin_minus v)
else number_of v)"
by (simp add: real_abs_def bin_arith_simps minus_real_number_of
less_real_number_of real_of_int_le_iff)