diff -r 8882d47e075f -r 2c01c0bdb385 src/HOL/Real/HahnBanach/Linearform.thy --- a/src/HOL/Real/HahnBanach/Linearform.thy Tue Jul 15 16:02:10 2008 +0200 +++ b/src/HOL/Real/HahnBanach/Linearform.thy Tue Jul 15 16:50:09 2008 +0200 @@ -20,9 +20,10 @@ declare linearform.intro [intro?] lemma (in linearform) neg [iff]: - includes vectorspace + assumes "vectorspace V" shows "x \ V \ f (- x) = - f x" proof - + interpret vectorspace [V] by fact assume x: "x \ V" hence "f (- x) = f ((- 1) \ x)" by (simp add: negate_eq1) also from x have "... = (- 1) * (f x)" by (rule mult) @@ -31,9 +32,10 @@ qed lemma (in linearform) diff [iff]: - includes vectorspace + assumes "vectorspace V" shows "x \ V \ y \ V \ f (x - y) = f x - f y" proof - + interpret vectorspace [V] by fact assume x: "x \ V" and y: "y \ V" hence "x - y = x + - y" by (rule diff_eq1) also have "f ... = f x + f (- y)" by (rule add) (simp_all add: x y) @@ -44,9 +46,10 @@ text {* Every linear form yields @{text 0} for the @{text 0} vector. *} lemma (in linearform) zero [iff]: - includes vectorspace + assumes "vectorspace V" shows "f 0 = 0" proof - + interpret vectorspace [V] by fact have "f 0 = f (0 - 0)" by simp also have "\ = f 0 - f 0" using `vectorspace V` by (rule diff) simp_all also have "\ = 0" by simp