1.1 --- a/src/HOL/Real/RealDef.thy Wed Dec 06 12:28:52 2000 +0100
1.2 +++ b/src/HOL/Real/RealDef.thy Wed Dec 06 12:34:12 2000 +0100
1.3 @@ -15,7 +15,7 @@
1.4
1.5
1.6 instance
1.7 - real :: {ord, zero, plus, times, minus}
1.8 + real :: {ord, zero, plus, times, minus, inverse}
1.9
1.10 consts
1.11
1.12 @@ -24,17 +24,24 @@
1.13 defs
1.14
1.15 real_zero_def
1.16 - "0 == Abs_real(realrel^^{(preal_of_prat(prat_of_pnat 1p),
1.17 + "0 == Abs_real(realrel^^{(preal_of_prat(prat_of_pnat 1p),
1.18 preal_of_prat(prat_of_pnat 1p))})"
1.19 real_one_def
1.20 - "1r == Abs_real(realrel^^{(preal_of_prat(prat_of_pnat 1p) +
1.21 + "1r == Abs_real(realrel^^{(preal_of_prat(prat_of_pnat 1p) +
1.22 preal_of_prat(prat_of_pnat 1p),preal_of_prat(prat_of_pnat 1p))})"
1.23
1.24 real_minus_def
1.25 - "- R == Abs_real(UN (x,y):Rep_real(R). realrel^^{(y,x)})"
1.26 + "- R == Abs_real(UN (x,y):Rep_real(R). realrel^^{(y,x)})"
1.27
1.28 - real_diff_def "x - y == x + (- y :: real)"
1.29 + real_diff_def
1.30 + "R - (S::real) == R + - S"
1.31
1.32 + real_inverse_def
1.33 + "inverse (R::real) == (@S. R ~= 0 & S*R = 1r)"
1.34 +
1.35 + real_divide_def
1.36 + "R / (S::real) == R * inverse S"
1.37 +
1.38 constdefs
1.39
1.40 real_of_preal :: preal => real
1.41 @@ -42,9 +49,6 @@
1.42 Abs_real(realrel^^{(m+preal_of_prat(prat_of_pnat 1p),
1.43 preal_of_prat(prat_of_pnat 1p))})"
1.44
1.45 - rinv :: real => real
1.46 - "rinv(R) == (@S. R ~= 0 & S*R = 1r)"
1.47 -
1.48 real_of_posnat :: nat => real
1.49 "real_of_posnat n == real_of_preal(preal_of_prat(prat_of_pnat(pnat_of_nat n)))"
1.50