--- a/src/HOL/Real/RealDef.thy Sat Dec 30 22:03:47 2000 +0100
+++ b/src/HOL/Real/RealDef.thy Sat Dec 30 22:13:18 2000 +0100
@@ -7,6 +7,9 @@
RealDef = PReal +
+instance preal :: order (preal_le_refl,preal_le_trans,preal_le_anti_sym,
+ preal_less_le)
+
constdefs
realrel :: "((preal * preal) * (preal * preal)) set"
"realrel == {p. ? x1 y1 x2 y2. p = ((x1,y1),(x2,y2)) & x1+y2 = x2+y1}"
@@ -18,8 +21,11 @@
real :: {ord, zero, plus, times, minus, inverse}
consts
+ "1r" :: real ("1r")
- "1r" :: real ("1r")
+ (*Overloaded constant: denotes the Real subset of enclosing types such as
+ hypreal and complex*)
+ SReal :: "'a set"
defs
@@ -58,18 +64,21 @@
defs
real_add_def
- "P + Q == Abs_real(UN p1:Rep_real(P). UN p2:Rep_real(Q).
- (%(x1,y1). (%(x2,y2). realrel^^{(x1+x2, y1+y2)}) p2) p1)"
+ "P+Q == Abs_real(UN p1:Rep_real(P). UN p2:Rep_real(Q).
+ (%(x1,y1). (%(x2,y2). realrel^^{(x1+x2, y1+y2)}) p2) p1)"
real_mult_def
- "P * Q == Abs_real(UN p1:Rep_real(P). UN p2:Rep_real(Q).
- (%(x1,y1). (%(x2,y2). realrel^^{(x1*x2+y1*y2,x1*y2+x2*y1)}) p2) p1)"
+ "P*Q == Abs_real(UN p1:Rep_real(P). UN p2:Rep_real(Q).
+ (%(x1,y1). (%(x2,y2). realrel^^{(x1*x2+y1*y2,x1*y2+x2*y1)})
+ p2) p1)"
real_less_def
- "P < Q == EX x1 y1 x2 y2. x1 + y2 < x2 + y1 &
- (x1,y1):Rep_real(P) &
- (x2,y2):Rep_real(Q)"
+ "P<Q == EX x1 y1 x2 y2. x1 + y2 < x2 + y1 &
+ (x1,y1):Rep_real(P) & (x2,y2):Rep_real(Q)"
real_le_def
"P <= (Q::real) == ~(Q < P)"
+syntax (symbols)
+ SReal :: "'a set" ("\\<real>")
+
end