--- a/src/HOL/Real.thy Fri Apr 02 13:33:48 2010 +0200
+++ b/src/HOL/Real.thy Wed Apr 07 19:17:10 2010 +0200
@@ -2,28 +2,4 @@
imports RComplete RealVector
begin
-lemma field_le_epsilon:
- fixes x y :: "'a:: {number_ring,division_by_zero,ordered_field}"
- assumes e: "(!!e. 0 < e ==> x \<le> y + e)"
- shows "x \<le> y"
-proof (rule ccontr)
- assume xy: "\<not> x \<le> y"
- hence "(x-y)/2 > 0"
- by (metis half_gt_zero le_iff_diff_le_0 linorder_not_le local.xy)
- hence "x \<le> y + (x - y) / 2"
- by (rule e [of "(x-y)/2"])
- also have "... = (x - y + 2*y)/2"
- by auto
- (metis add_less_cancel_left add_numeral_0_right class_semiring.add_c xy e
- diff_add_cancel gt_half_sum less_half_sum linorder_not_le number_of_Pls)
- also have "... = (x + y) / 2"
- by auto
- also have "... < x" using xy
- by auto
- finally have "x<x" .
- thus False
- by auto
-qed
-
-
end