(* Title: HOL/Real/real_arith.ML
ID: $Id: real_arith.ML,v 1.42 2007/07/31 17:40:25 wenzelm Exp $
Author: Tobias Nipkow, TU Muenchen
Copyright 1999 TU Muenchen
Simprocs for common factor cancellation & Rational coefficient handling
Instantiation of the generic linear arithmetic package for type real.
*)
local
val simps = [@{thm real_of_nat_zero}, @{thm real_of_nat_Suc}, @{thm real_of_nat_add},
@{thm real_of_nat_mult}, @{thm real_of_int_zero}, @{thm real_of_one},
@{thm real_of_int_add}, @{thm real_of_int_minus}, @{thm real_of_int_diff},
@{thm real_of_int_mult}, @{thm real_of_int_of_nat_eq},
@{thm real_of_nat_number_of}, @{thm real_number_of}]
val nat_inj_thms = [@{thm real_of_nat_le_iff} RS iffD2,
@{thm real_of_nat_inject} RS iffD2]
(* not needed because x < (y::nat) can be rewritten as Suc x <= y:
real_of_nat_less_iff RS iffD2 *)
val int_inj_thms = [@{thm real_of_int_le_iff} RS iffD2,
@{thm real_of_int_inject} RS iffD2]
(* not needed because x < (y::int) can be rewritten as x + 1 <= y:
real_of_int_less_iff RS iffD2 *)
in
val real_arith_setup =
LinArith.map_data (fn {add_mono_thms, mult_mono_thms, inj_thms, lessD, neqE, simpset} =>
{add_mono_thms = add_mono_thms,
mult_mono_thms = mult_mono_thms,
inj_thms = int_inj_thms @ nat_inj_thms @ inj_thms,
lessD = lessD, (*Can't change lessD: the reals are dense!*)
neqE = neqE,
simpset = simpset addsimps simps}) #>
arith_inj_const ("RealDef.real", HOLogic.natT --> HOLogic.realT) #>
arith_inj_const ("RealDef.real", HOLogic.intT --> HOLogic.realT)
end;