diff -r 915da29bf5d9 -r 7e741e22d7fc src/HOL/Probability/Information.thy --- a/src/HOL/Probability/Information.thy Thu Jun 25 22:56:33 2015 +0200 +++ b/src/HOL/Probability/Information.thy Thu Jun 25 23:33:47 2015 +0200 @@ -1022,11 +1022,12 @@ Pxyz x * log b (Pxz (fst x, snd (snd x)) / (Px (fst x) * Pz (snd (snd x)))) = Pxyz x * log b (Pxyz x * Pz (snd (snd x)) / (Pxz (fst x, snd (snd x)) * Pyz (snd x))) " proof eventually_elim - case (goal1 x) + case (elim x) show ?case proof cases assume "Pxyz x \ 0" - with goal1 have "0 < Px (fst x)" "0 < Pz (snd (snd x))" "0 < Pxz (fst x, snd (snd x))" "0 < Pyz (snd x)" "0 < Pxyz x" + with elim have "0 < Px (fst x)" "0 < Pz (snd (snd x))" "0 < Pxz (fst x, snd (snd x))" + "0 < Pyz (snd x)" "0 < Pxyz x" by auto then show ?thesis using b_gt_1 by (simp add: log_simps less_imp_le field_simps) @@ -1252,11 +1253,12 @@ Pxyz x * log b (Pxz (fst x, snd (snd x)) / (Px (fst x) * Pz (snd (snd x)))) = Pxyz x * log b (Pxyz x * Pz (snd (snd x)) / (Pxz (fst x, snd (snd x)) * Pyz (snd x))) " proof eventually_elim - case (goal1 x) + case (elim x) show ?case proof cases assume "Pxyz x \ 0" - with goal1 have "0 < Px (fst x)" "0 < Pz (snd (snd x))" "0 < Pxz (fst x, snd (snd x))" "0 < Pyz (snd x)" "0 < Pxyz x" + with elim have "0 < Px (fst x)" "0 < Pz (snd (snd x))" "0 < Pxz (fst x, snd (snd x))" + "0 < Pyz (snd x)" "0 < Pxyz x" by auto then show ?thesis using b_gt_1 by (simp add: log_simps less_imp_le field_simps) @@ -1730,11 +1732,11 @@ Pxy x * log b (Pxy x / (Px (fst x) * Py (snd x)))" (is "AE x in _. ?f x = ?g x") proof eventually_elim - case (goal1 x) + case (elim x) show ?case proof cases assume "Pxy x \ 0" - with goal1 have "0 < Px (fst x)" "0 < Py (snd x)" "0 < Pxy x" + with elim have "0 < Px (fst x)" "0 < Py (snd x)" "0 < Pxy x" by auto then show ?thesis using b_gt_1 by (simp add: log_simps less_imp_le field_simps)