# HG changeset patch
# User huffman
# Date 1315501673 25200
# Node ID e9d1fcbc7d20c4d01ee5cac40e47b4654d336e73
# Parent  f74a4175a3a8bef0552bc03281711d0f76dbfe61
remove unnecessary intermediate lemmas

diff -r f74a4175a3a8 -r e9d1fcbc7d20 src/HOL/Complex.thy
--- 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)
diff -r f74a4175a3a8 -r e9d1fcbc7d20 src/HOL/NSA/NSComplex.thy
--- 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)