diff -r 0035be079bee -r ead82c82da9e src/HOL/ex/Commutative_Ring_Complete.thy --- a/src/HOL/ex/Commutative_Ring_Complete.thy Wed Jun 13 16:43:02 2007 +0200 +++ b/src/HOL/ex/Commutative_Ring_Complete.thy Wed Jun 13 18:30:11 2007 +0200 @@ -150,7 +150,7 @@ then obtain d where X:"x=Suc (Suc d)" .. from prems have NR:"isnorm R" "isnorm P2" by (auto simp add: norm_Pinj[of _ P2] norm_PX2[of Q2 y R]) with prems have "isnorm (Pinj (x - 1) P2)" by(cases P2, auto) - with prems NR have "isnorm (R \ Pinj (x - 1) P2)" "isnorm (PX Q2 y R)" by simp + with prems NR have "isnorm (R \ Pinj (x - 1) P2)" "isnorm (PX Q2 y R)" by simp assumption with X have ?case by (simp add: norm_PXtrans[of Q2 y _]) } ultimately show ?case by blast next @@ -168,7 +168,7 @@ then obtain d where X:"x=Suc (Suc d)" .. from prems have NR:"isnorm R" "isnorm P2" by (auto simp add: norm_Pinj[of _ P2] norm_PX2[of Q2 y R]) with prems have "isnorm (Pinj (x - 1) P2)" by(cases P2, auto) - with prems NR have "isnorm (R \ Pinj (x - 1) P2)" "isnorm (PX Q2 y R)" by simp + with prems NR have "isnorm (R \ Pinj (x - 1) P2)" "isnorm (PX Q2 y R)" by simp assumption with X have ?case by (simp add: norm_PXtrans[of Q2 y _]) } ultimately show ?case by blast next