diff options
Diffstat (limited to 'plugins/setoid_ring/RealField.v')
| -rw-r--r-- | plugins/setoid_ring/RealField.v | 31 |
1 files changed, 25 insertions, 6 deletions
diff --git a/plugins/setoid_ring/RealField.v b/plugins/setoid_ring/RealField.v index 29372212..38bc58a6 100644 --- a/plugins/setoid_ring/RealField.v +++ b/plugins/setoid_ring/RealField.v @@ -1,3 +1,13 @@ +(************************************************************************) +(* * The Coq Proof Assistant / The Coq Development Team *) +(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *) +(* <O___,, * (see CREDITS file for the list of authors) *) +(* \VV/ **************************************************************) +(* // * This file is distributed under the terms of the *) +(* * GNU Lesser General Public License Version 2.1 *) +(* * (see LICENSE file for the text of the license) *) +(************************************************************************) + Require Import Nnat. Require Import ArithRing. Require Export Ring Field. @@ -59,11 +69,12 @@ Notation Rset := (Eqsth R). Notation Rext := (Eq_ext Rplus Rmult Ropp). Lemma Rlt_0_2 : 0 < 2. +Proof. apply Rlt_trans with (0 + 1). apply Rlt_n_Sn. rewrite Rplus_comm. apply Rplus_lt_compat_l. - replace 1 with (0 + 1). + replace R1 with (0 + 1). apply Rlt_n_Sn. apply Rplus_0_l. Qed. @@ -126,9 +137,17 @@ Ltac Rpow_tac t := | _ => constr:(N.of_nat t) end. -Add Field RField : Rfield - (completeness Zeq_bool_complete, power_tac R_power_theory [Rpow_tac]). - - - +Ltac IZR_tac t := + match t with + | R0 => constr:(0%Z) + | R1 => constr:(1%Z) + | IZR ?u => + match isZcst u with + | true => u + | _ => constr:(InitialRing.NotConstant) + end + | _ => constr:(InitialRing.NotConstant) + end. +Add Field RField : Rfield + (completeness Zeq_bool_complete, constants [IZR_tac], power_tac R_power_theory [Rpow_tac]). |