--- a/src/HOL/Real/PRat.thy Fri Aug 27 15:42:10 1999 +0200
+++ b/src/HOL/Real/PRat.thy Fri Aug 27 15:43:53 1999 +0200
@@ -11,7 +11,7 @@
ratrel :: "((pnat * pnat) * (pnat * pnat)) set"
"ratrel == {p. ? x1 y1 x2 y2. p=((x1::pnat,y1),(x2,y2)) & x1*y2 = x2*y1}"
-typedef prat = "{x::(pnat*pnat).True}/ratrel" (Equiv.quotient_def)
+typedef prat = "UNIV/ratrel" (Equiv.quotient_def)
instance
prat :: {ord,plus,times}
@@ -28,12 +28,12 @@
defs
prat_add_def
- "P + Q == Abs_prat(UN p1:Rep_prat(P). UN p2:Rep_prat(Q).
- split(%x1 y1. split(%x2 y2. ratrel^^{(x1*y2 + x2*y1, y1*y2)}) p2) p1)"
+ "P + Q == Abs_prat(UN (x1,y1):Rep_prat(P). UN (x2,y2):Rep_prat(Q).
+ ratrel^^{(x1*y2 + x2*y1, y1*y2)})"
prat_mult_def
- "P * Q == Abs_prat(UN p1:Rep_prat(P). UN p2:Rep_prat(Q).
- split(%x1 y1. split(%x2 y2. ratrel^^{(x1*x2, y1*y2)}) p2) p1)"
+ "P * Q == Abs_prat(UN (x1,y1):Rep_prat(P). UN (x2,y2):Rep_prat(Q).
+ ratrel^^{(x1*x2, y1*y2)})"
(*** Gleason p. 119 ***)
prat_less_def