src/HOL/Probability/Distributions.thy
 changeset 56381 0556204bc230 parent 56371 fb9ae0727548 child 56536 aefb4a8da31f
--- a/src/HOL/Probability/Distributions.thy	Thu Apr 03 17:16:02 2014 +0200
+++ b/src/HOL/Probability/Distributions.thy	Thu Apr 03 17:56:08 2014 +0200
@@ -52,7 +52,7 @@
let ?F = "\<lambda>x. - exp (- x * l)"

have deriv: "\<And>x. DERIV ?F x :> ?f x" "\<And>x. 0 \<le> l * exp (- x * l)"
-    by (auto intro!: DERIV_intros simp: zero_le_mult_iff)
+    by (auto intro!: derivative_eq_intros simp: zero_le_mult_iff)

have "emeasure ?D (space ?D) = (\<integral>\<^sup>+ x. ereal (?f x) * indicator {0..} x \<partial>lborel)"
by (auto simp: emeasure_density exponential_density_def
@@ -178,12 +178,12 @@
proof (rule integral_FTC_atLeastAtMost)
fix x assume "0 \<le> x" "x \<le> b"
show "DERIV (\<lambda>x. x * exp (-x)) x :> exp (-x) - x * exp (-x)"
-        by (auto intro!: DERIV_intros)
+        by (auto intro!: derivative_eq_intros)
show "isCont (\<lambda>x. exp (- x) - x * exp (- x)) x "
by (intro continuous_intros)
qed fact
also have "(\<integral>x. (exp (-x)) * indicator {0 .. b} x \<partial>lborel) = - exp (- b) - - exp (- 0)"
-      by (rule integral_FTC_atLeastAtMost) (auto intro!: DERIV_intros)
+      by (rule integral_FTC_atLeastAtMost) (auto intro!: derivative_eq_intros)
finally show "1 - (inverse (exp b) + b / exp b) = integral\<^sup>L lborel (?f b)"
by (auto simp: field_simps exp_minus inverse_eq_divide)
qed
@@ -374,7 +374,7 @@
fix x
show "DERIV (\<lambda>x. x\<^sup>2 / (2 * measure lborel {a..b})) x :> x / measure lborel {a..b}"
using uniform_distributed_params[OF D]
-      by (auto intro!: DERIV_intros)
+      by (auto intro!: derivative_eq_intros)
show "isCont (\<lambda>x. x / Sigma_Algebra.measure lborel {a..b}) x"
using uniform_distributed_params[OF D]
by (auto intro!: isCont_divide)