uniform Generic_Target.standard_declaration, which uses the standard morphism for each context (NB: targets like "interpretation" appear like "theory" but declare local type parameters);
uniform treatment of target contexts as invisible;
added Local_Theory.standard_form convenience;
(* Title: HOL/ex/Arithmetic_Series_Complex.thy
Author: Benjamin Porter, 2006
*)
header {* Arithmetic Series for Reals *}
theory Arithmetic_Series_Complex
imports Complex_Main
begin
lemma arith_series_real:
"(2::real) * (\<Sum>i\<in>{..<n}. a + of_nat i * d) =
of_nat n * (a + (a + of_nat(n - 1)*d))"
proof -
have
"((1::real) + 1) * (\<Sum>i\<in>{..<n}. a + of_nat(i)*d) =
of_nat(n) * (a + (a + of_nat(n - 1)*d))"
by (rule arith_series_general)
thus ?thesis by simp
qed
end