diff options
| author |  Guillaume Melquiond <guillaume.melquiond@inria.fr> | 2017-03-05 21:50:19 +0100 |
|---|---|---|
| committer |  Maxime Dénès <mail@maximedenes.fr> | 2017-03-22 17:56:02 +0100 |
| commit | 4e6fa17a3ef0b8d12cb8d55305f302338589ad1c (patch) | |
| tree | b6ed89f849f9423c9a2b3bee42bd8b9f5b176305 /theories/Reals/RIneq.v | |
| parent | d6ced637d9b7acabef2ccc9e761ec149bc7c93da (diff) | |
Make IZR a morphism for field.
There are now two field structures for R: one in RealField and one in
RIneq. The first one is used to prove that IZR is a morphism which is
needed to define the second one.
Diffstat (limited to 'theories/Reals/RIneq.v')
| -rw-r--r-- | theories/Reals/RIneq.v | 25 |
1 files changed, 25 insertions, 0 deletions
diff --git a/theories/Reals/RIneq.v b/theories/Reals/RIneq.v index 7cd4c00c7..dd2108159 100644 --- a/theories/Reals/RIneq.v +++ b/theories/Reals/RIneq.v @@ -2016,6 +2016,31 @@ Proof. [ apply not_0_INR; discriminate | unfold INR; ring ]. Qed. +Lemma R_rm : ring_morph + R0 R1 Rplus Rmult Rminus Ropp eq + 0%Z 1%Z Zplus Zmult Zminus Zopp Zeq_bool IZR. +Proof. +constructor ; try easy. +exact plus_IZR. +exact minus_IZR. +exact mult_IZR. +exact opp_IZR. +intros x y H. +apply f_equal. +now apply Zeq_bool_eq. +Qed. + +Lemma Zeq_bool_IZR x y : + IZR x = IZR y -> Zeq_bool x y = true. +Proof. +intros H. +apply Zeq_is_eq_bool. +now apply eq_IZR. +Qed. + +Add Field RField : Rfield + (completeness Zeq_bool_IZR, morphism R_rm, constants [IZR_tac], power_tac R_power_theory [Rpow_tac]). + (*********************************************************) (** ** Other rules about < and <= *) (*********************************************************) |