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Diffstat (limited to 'theories/Reals/Rdefinitions.v')
| -rw-r--r-- | theories/Reals/Rdefinitions.v | 29 |
1 files changed, 29 insertions, 0 deletions
diff --git a/theories/Reals/Rdefinitions.v b/theories/Reals/Rdefinitions.v index f3f8f7409..cb5dea93a 100644 --- a/theories/Reals/Rdefinitions.v +++ b/theories/Reals/Rdefinitions.v @@ -69,3 +69,32 @@ Notation "x <= y <= z" := (x <= y /\ y <= z) : R_scope. Notation "x <= y < z" := (x <= y /\ y < z) : R_scope. Notation "x < y < z" := (x < y /\ y < z) : R_scope. Notation "x < y <= z" := (x < y /\ y <= z) : R_scope. + +(**********************************************************) +(** * Injection from [Z] to [R] *) +(**********************************************************) + +(* compact representation for 2*p *) +Fixpoint IPR_2 (p:positive) : R := + match p with + | xH => R1 + R1 + | xO p => (R1 + R1) * IPR_2 p + | xI p => (R1 + R1) * (R1 + IPR_2 p) + end. + +Definition IPR (p:positive) : R := + match p with + | xH => R1 + | xO p => IPR_2 p + | xI p => R1 + IPR_2 p + end. +Arguments IPR p%positive : simpl never. + +(**********) +Definition IZR (z:Z) : R := + match z with + | Z0 => R0 + | Zpos n => IPR n + | Zneg n => - IPR n + end. +Arguments IZR z%Z : simpl never. |