summaryrefslogtreecommitdiff
path: root/theories7/Reals/DiscrR.v
diff options
context:
space:
mode:
Diffstat (limited to 'theories7/Reals/DiscrR.v')
-rw-r--r--theories7/Reals/DiscrR.v58
1 files changed, 0 insertions, 58 deletions
diff --git a/theories7/Reals/DiscrR.v b/theories7/Reals/DiscrR.v
deleted file mode 100644
index 31c90727..00000000
--- a/theories7/Reals/DiscrR.v
+++ /dev/null
@@ -1,58 +0,0 @@
-(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
-(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(************************************************************************)
-
-(*i $Id: DiscrR.v,v 1.1.2.1 2004/07/16 19:31:32 herbelin Exp $ i*)
-
-Require RIneq.
-Require Omega.
-V7only [Import R_scope.]. Open Local Scope R_scope.
-
-Lemma Rlt_R0_R2 : ``0<2``.
-Replace ``2`` with (INR (2)); [Apply lt_INR_0; Apply lt_O_Sn | Reflexivity].
-Qed.
-
-Lemma Rplus_lt_pos : (x,y:R) ``0<x`` -> ``0<y`` -> ``0<x+y``.
-Intros.
-Apply Rlt_trans with x.
-Assumption.
-Pattern 1 x; Rewrite <- Rplus_Or.
-Apply Rlt_compatibility.
-Assumption.
-Qed.
-
-Lemma IZR_eq : (z1,z2:Z) z1=z2 -> (IZR z1)==(IZR z2).
-Intros; Rewrite H; Reflexivity.
-Qed.
-
-Lemma IZR_neq : (z1,z2:Z) `z1<>z2` -> ``(IZR z1)<>(IZR z2)``.
-Intros; Red; Intro; Elim H; Apply eq_IZR; Assumption.
-Qed.
-
-Tactic Definition DiscrR :=
- Try Match Context With
- | [ |- ~(?1==?2) ] -> Replace ``2`` with (IZR `2`); [Replace R1 with (IZR `1`); [Replace R0 with (IZR `0`); [Repeat Rewrite <- plus_IZR Orelse Rewrite <- mult_IZR Orelse Rewrite <- Ropp_Ropp_IZR Orelse Rewrite Z_R_minus; Apply IZR_neq; Try Discriminate | Reflexivity] | Reflexivity] | Reflexivity].
-
-Recursive Tactic Definition Sup0 :=
- Match Context With
- | [ |- ``0<1`` ] -> Apply Rlt_R0_R1
- | [ |- ``0<?1`` ] -> Repeat (Apply Rmult_lt_pos Orelse Apply Rplus_lt_pos; Try Apply Rlt_R0_R1 Orelse Apply Rlt_R0_R2)
- | [ |- ``?1>0`` ] -> Change ``0<?1``; Sup0.
-
-Tactic Definition SupOmega := Replace ``2`` with (IZR `2`); [Replace R1 with (IZR `1`); [Replace R0 with (IZR `0`); [Repeat Rewrite <- plus_IZR Orelse Rewrite <- mult_IZR Orelse Rewrite <- Ropp_Ropp_IZR Orelse Rewrite Z_R_minus; Apply IZR_lt; Omega | Reflexivity] | Reflexivity] | Reflexivity].
-
-Recursive Tactic Definition Sup :=
- Match Context With
- | [ |- (Rgt ?1 ?2) ] -> Change ``?2<?1``; Sup
- | [ |- ``0<?1`` ] -> Sup0
- | [ |- (Rlt (Ropp ?1) R0) ] -> Rewrite <- Ropp_O; Sup
- | [ |- (Rlt (Ropp ?1) (Ropp ?2)) ] -> Apply Rlt_Ropp; Sup
- | [ |- (Rlt (Ropp ?1) ?2) ] -> Apply Rlt_trans with ``0``; Sup
- | [ |- (Rlt ?1 ?2) ] -> SupOmega
- | _ -> Idtac.
-
-Tactic Definition RCompute := Replace ``2`` with (IZR `2`); [Replace R1 with (IZR `1`); [Replace R0 with (IZR `0`); [Repeat Rewrite <- plus_IZR Orelse Rewrite <- mult_IZR Orelse Rewrite <- Ropp_Ropp_IZR Orelse Rewrite Z_R_minus; Apply IZR_eq; Try Reflexivity | Reflexivity] | Reflexivity] | Reflexivity].