diff -r bb20f11dd842 -r 1bf7b186542e src/HOL/Probability/Projective_Family.thy --- a/src/HOL/Probability/Projective_Family.thy Mon Nov 09 13:49:56 2015 +0100 +++ b/src/HOL/Probability/Projective_Family.thy Mon Nov 09 15:48:17 2015 +0100 @@ -97,7 +97,7 @@ by simp qed (force simp: generator.simps prod_emb_empty[symmetric]) -interpretation generator!: algebra "space (PiM I M)" generator +interpretation generator: algebra "space (PiM I M)" generator by (rule algebra_generator) lemma sets_PiM_generator: "sets (PiM I M) = sigma_sets (space (PiM I M)) generator" @@ -407,7 +407,7 @@ definition CI :: "nat set \ (nat \ 'a) measure" where "CI J = distr (C 0 (up_to J) (\x. undefined)) (PiM J M) (\f. restrict f J)" -sublocale PF!: projective_family UNIV CI +sublocale PF: projective_family UNIV CI unfolding projective_family_def proof safe show "finite J \ prob_space (CI J)" for J @@ -460,7 +460,7 @@ also have "\ \ (INF i. C 0 i (\x. undefined) (X i))" proof (intro INF_greatest) fix n - interpret C!: prob_space "C 0 n (\x. undefined)" + interpret C: prob_space "C 0 n (\x. undefined)" by (rule prob_space_C) simp show "(INF i. CI (J i) (X' i)) \ C 0 n (\x. undefined) (X n)" proof cases @@ -606,9 +606,9 @@ using count by (auto simp: t_def) then have inj_t_J: "inj_on t (J i)" for i by (rule subset_inj_on) auto - interpret IT!: Ionescu_Tulcea "\i \. M (f i)" "\i. M (f i)" + interpret IT: Ionescu_Tulcea "\i \. M (f i)" "\i. M (f i)" by standard auto - interpret Mf!: product_prob_space "\x. M (f x)" UNIV + interpret Mf: product_prob_space "\x. M (f x)" UNIV by standard have C_eq_PiM: "IT.C 0 n (\_. undefined) = PiM {0..x. M (f x))" for n proof (induction n)