--- a/src/HOL/Complex.thy Thu Sep 08 08:41:28 2011 -0700
+++ b/src/HOL/Complex.thy Thu Sep 08 10:07:53 2011 -0700
@@ -746,14 +746,6 @@
lemma rcis_cmod_arg: "rcis (cmod z) (arg z) = z"
by (cases "z = 0", simp_all add: rcis_def cis_arg sgn_div_norm of_real_def)
-lemma cos_arg_i_mult_zero_pos: (* TODO: delete *)
- "0 < y ==> cos (arg(Complex 0 y)) = 0"
- using cis_arg [of "Complex 0 y"] by (simp add: complex_eq_iff)
-
-lemma cos_arg_i_mult_zero_neg: (* TODO: delete *)
- "y < 0 ==> cos (arg(Complex 0 y)) = 0"
- using cis_arg [of "Complex 0 y"] by (simp add: complex_eq_iff)
-
lemma cos_arg_i_mult_zero [simp]:
"y \<noteq> 0 ==> cos (arg(Complex 0 y)) = 0"
using cis_arg [of "Complex 0 y"] by (simp add: complex_eq_iff)
--- a/src/HOL/NSA/NSComplex.thy Thu Sep 08 08:41:28 2011 -0700
+++ b/src/HOL/NSA/NSComplex.thy Thu Sep 08 10:07:53 2011 -0700
@@ -457,14 +457,6 @@
(* harg *)
(*---------------------------------------------------------------------------*)
-lemma cos_harg_i_mult_zero_pos:
- "!!y. 0 < y ==> ( *f* cos) (harg(HComplex 0 y)) = 0"
-by transfer (rule cos_arg_i_mult_zero_pos)
-
-lemma cos_harg_i_mult_zero_neg:
- "!!y. y < 0 ==> ( *f* cos) (harg(HComplex 0 y)) = 0"
-by transfer (rule cos_arg_i_mult_zero_neg)
-
lemma cos_harg_i_mult_zero [simp]:
"!!y. y \<noteq> 0 ==> ( *f* cos) (harg(HComplex 0 y)) = 0"
by transfer (rule cos_arg_i_mult_zero)