1.1 --- a/src/HOL/Complex.thy Thu Sep 08 07:06:59 2011 -0700
1.2 +++ b/src/HOL/Complex.thy Thu Sep 08 07:16:47 2011 -0700
1.3 @@ -549,12 +549,6 @@
1.4 lemma Im_sgn [simp]: "Im(sgn z) = Im(z)/cmod z"
1.5 by (simp add: complex_sgn_def divide_inverse)
1.6
1.7 -lemma complex_inverse_complex_split:
1.8 - "inverse(complex_of_real x + ii * complex_of_real y) =
1.9 - complex_of_real(x/(x ^ 2 + y ^ 2)) -
1.10 - ii * complex_of_real(y/(x ^ 2 + y ^ 2))"
1.11 - by (simp add: complex_of_real_def i_def diff_minus divide_inverse)
1.12 -
1.13 (*----------------------------------------------------------------------------*)
1.14 (* Many of the theorems below need to be moved elsewhere e.g. Transc. Also *)
1.15 (* many of the theorems are not used - so should they be kept? *)
2.1 --- a/src/HOL/NSA/NSComplex.thy Thu Sep 08 07:06:59 2011 -0700
2.2 +++ b/src/HOL/NSA/NSComplex.thy Thu Sep 08 07:16:47 2011 -0700
2.3 @@ -434,12 +434,6 @@
2.4 lemma hIm_hsgn [simp]: "!!z. hIm(hsgn z) = hIm(z)/hcmod z"
2.5 by transfer (rule Im_sgn)
2.6
2.7 -lemma hcomplex_inverse_complex_split:
2.8 - "!!x y. inverse(hcomplex_of_hypreal x + iii * hcomplex_of_hypreal y) =
2.9 - hcomplex_of_hypreal(x/(x ^ 2 + y ^ 2)) -
2.10 - iii * hcomplex_of_hypreal(y/(x ^ 2 + y ^ 2))"
2.11 -by transfer (rule complex_inverse_complex_split)
2.12 -
2.13 lemma HComplex_inverse:
2.14 "!!x y. inverse (HComplex x y) =
2.15 HComplex (x/(x ^ 2 + y ^ 2)) (-y/(x ^ 2 + y ^ 2))"