author paulson Tue, 22 Feb 2005 13:05:47 +0100 changeset 15544 5f3ef1ddda1f parent 15543 0024472afce7 child 15545 0efa7126003f
removed redundant lemmas and simprules
```--- a/src/HOL/Hyperreal/Transcendental.thy	Tue Feb 22 10:54:30 2005 +0100
+++ b/src/HOL/Hyperreal/Transcendental.thy	Tue Feb 22 13:05:47 2005 +0100
@@ -158,9 +158,6 @@
done

-lemma real_mult_self_eq_zero_iff [simp]: "(r * r = 0) = (r = (0::real))"
-by auto
-
lemma real_sqrt_gt_zero: "0 < x ==> 0 < sqrt(x)"
apply (drule realpow_pos_nth2 [where n=1], safe)
@@ -2222,10 +2219,10 @@
done

-lemma real_sqrt_sum_squares_eq_cancel [simp]: "sqrt(x\<twosuperior> + y\<twosuperior>) = x ==> y = 0"
+lemma real_sqrt_sum_squares_eq_cancel: "sqrt(x\<twosuperior> + y\<twosuperior>) = x ==> y = 0"
by (drule_tac f = "%x. x\<twosuperior>" in arg_cong, auto)

-lemma real_sqrt_sum_squares_eq_cancel2 [simp]: "sqrt(x\<twosuperior> + y\<twosuperior>) = y ==> x = 0"
+lemma real_sqrt_sum_squares_eq_cancel2: "sqrt(x\<twosuperior> + y\<twosuperior>) = y ==> x = 0"
apply (rule_tac x = y in real_sqrt_sum_squares_eq_cancel)
done
@@ -2610,7 +2607,6 @@
val real_pow_sqrt_eq_sqrt_abs_pow2 = thm "real_pow_sqrt_eq_sqrt_abs_pow2";
val real_sqrt_pow_abs = thm "real_sqrt_pow_abs";
val not_real_square_gt_zero = thm "not_real_square_gt_zero";
-val real_mult_self_eq_zero_iff = thm "real_mult_self_eq_zero_iff";
val real_sqrt_gt_zero = thm "real_sqrt_gt_zero";
val real_sqrt_ge_zero = thm "real_sqrt_ge_zero";
val sqrt_eqI = thm "sqrt_eqI";
@@ -2853,8 +2849,6 @@
val real_sqrt_sum_squares_gt_zero2 = thm "real_sqrt_sum_squares_gt_zero2";
val real_sqrt_sum_squares_gt_zero3 = thm "real_sqrt_sum_squares_gt_zero3";
val real_sqrt_sum_squares_gt_zero3a = thm "real_sqrt_sum_squares_gt_zero3a";
-val real_sqrt_sum_squares_eq_cancel = thm "real_sqrt_sum_squares_eq_cancel";
-val real_sqrt_sum_squares_eq_cancel2 = thm "real_sqrt_sum_squares_eq_cancel2";
val cos_x_y_ge_minus_one = thm "cos_x_y_ge_minus_one";
val cos_x_y_ge_minus_one1a = thm "cos_x_y_ge_minus_one1a";
val cos_x_y_le_one = thm "cos_x_y_le_one";```