diff -r 206d779ba96d -r ee6cd48cf840 src/HOL/Real/RealDef.thy --- a/src/HOL/Real/RealDef.thy Mon Feb 21 18:04:28 2005 +0100 +++ b/src/HOL/Real/RealDef.thy Mon Feb 21 19:23:46 2005 +0100 @@ -353,7 +353,7 @@ done lemma real_le_anti_sym: "[| z \ w; w \ z |] ==> z = (w::real)" -by (cases z, cases w, simp add: real_le order_antisym) +by (cases z, cases w, simp add: real_le) lemma real_trans_lemma: assumes "x + v \ u + y" @@ -368,7 +368,7 @@ by (simp add: preal_add_le_cancel_left prems) also have "... = (u'+y) + (u+v)" by (simp add: preal_add_ac) finally show ?thesis by (simp add: preal_add_le_cancel_right) -qed +qed lemma real_le_trans: "[| i \ j; j \ k |] ==> i \ (k::real)" apply (cases i, cases j, cases k) @@ -401,7 +401,7 @@ apply (auto simp add: real_le real_zero_def real_diff_def real_add real_minus preal_add_ac) apply (simp_all add: preal_add_assoc [symmetric] preal_cancels) -done +done lemma real_add_left_mono: assumes le: "x \ y" shows "z + x \ z + (y::real)"