--- a/src/HOL/Complex.thy Thu Sep 08 07:06:59 2011 -0700
+++ b/src/HOL/Complex.thy Thu Sep 08 07:16:47 2011 -0700
@@ -549,12 +549,6 @@
lemma Im_sgn [simp]: "Im(sgn z) = Im(z)/cmod z"
by (simp add: complex_sgn_def divide_inverse)
-lemma complex_inverse_complex_split:
- "inverse(complex_of_real x + ii * complex_of_real y) =
- complex_of_real(x/(x ^ 2 + y ^ 2)) -
- ii * complex_of_real(y/(x ^ 2 + y ^ 2))"
- by (simp add: complex_of_real_def i_def diff_minus divide_inverse)
-
(*----------------------------------------------------------------------------*)
(* Many of the theorems below need to be moved elsewhere e.g. Transc. Also *)
(* many of the theorems are not used - so should they be kept? *)
--- a/src/HOL/NSA/NSComplex.thy Thu Sep 08 07:06:59 2011 -0700
+++ b/src/HOL/NSA/NSComplex.thy Thu Sep 08 07:16:47 2011 -0700
@@ -434,12 +434,6 @@
lemma hIm_hsgn [simp]: "!!z. hIm(hsgn z) = hIm(z)/hcmod z"
by transfer (rule Im_sgn)
-lemma hcomplex_inverse_complex_split:
- "!!x y. inverse(hcomplex_of_hypreal x + iii * hcomplex_of_hypreal y) =
- hcomplex_of_hypreal(x/(x ^ 2 + y ^ 2)) -
- iii * hcomplex_of_hypreal(y/(x ^ 2 + y ^ 2))"
-by transfer (rule complex_inverse_complex_split)
-
lemma HComplex_inverse:
"!!x y. inverse (HComplex x y) =
HComplex (x/(x ^ 2 + y ^ 2)) (-y/(x ^ 2 + y ^ 2))"