diff options
Diffstat (limited to 'theories/Reals/Raxioms.v')
-rw-r--r-- | theories/Reals/Raxioms.v | 22 |
1 files changed, 19 insertions, 3 deletions
diff --git a/theories/Reals/Raxioms.v b/theories/Reals/Raxioms.v index 9fbda92a2..e9098104c 100644 --- a/theories/Reals/Raxioms.v +++ b/theories/Reals/Raxioms.v @@ -118,14 +118,30 @@ Arguments INR n%nat. (** * Injection from [Z] to [R] *) (**********************************************************) +(* compact representation for 2*p *) +Fixpoint IPR_2 (p:positive) : R := + match p with + | xH => 1 + 1 + | xO p => (1 + 1) * IPR_2 p + | xI p => (1 + 1) * (1 + IPR_2 p) + end. + +Definition IPR (p:positive) : R := + match p with + | xH => 1 + | xO p => IPR_2 p + | xI p => 1 + IPR_2 p + end. +Arguments IPR p%positive : simpl never. + (**********) Definition IZR (z:Z) : R := match z with | Z0 => 0 - | Zpos n => INR (Pos.to_nat n) - | Zneg n => - INR (Pos.to_nat n) + | Zpos n => IPR n + | Zneg n => - IPR n end. -Arguments IZR z%Z. +Arguments IZR z%Z : simpl never. (**********************************************************) (** * [R] Archimedean *) |