1 files changed, 0 insertions, 134 deletions
diff --git a/contrib/setoid_ring/RealField.v b/contrib/setoid_ring/RealField.v
deleted file mode 100644
index 60641bcf..00000000
--- a/contrib/setoid_ring/RealField.v
+++ /dev/null
@@ -1,134 +0,0 @@
-Require Import Nnat.
-Require Import ArithRing. 
-Require Export Ring Field.
-Require Import Rdefinitions.
-Require Import Rpow_def.
-Require Import Raxioms.
-
-Open Local Scope R_scope.
-
-Lemma RTheory : ring_theory 0 1 Rplus Rmult Rminus Ropp (eq (A:=R)).
-Proof.
-constructor.
- intro; apply Rplus_0_l.
- exact Rplus_comm.
- symmetry  in |- *; apply Rplus_assoc.
- intro; apply Rmult_1_l.
- exact Rmult_comm.
- symmetry  in |- *; apply Rmult_assoc.
- intros m n p.
-   rewrite Rmult_comm in |- *.
-   rewrite (Rmult_comm n p) in |- *.
-   rewrite (Rmult_comm m p) in |- *.
-   apply Rmult_plus_distr_l.
- reflexivity.
- exact Rplus_opp_r.
-Qed.
-
-Lemma Rfield : field_theory 0 1 Rplus Rmult Rminus Ropp Rdiv Rinv (eq(A:=R)).
-Proof.
-constructor.
- exact RTheory.
- exact R1_neq_R0.
- reflexivity.
- exact Rinv_l.
-Qed.
-
-Lemma Rlt_n_Sn : forall x, x < x + 1.
-Proof.
-intro.
-elim archimed with x; intros.
-destruct H0.
- apply Rlt_trans with (IZR (up x)); trivial.
-    replace (IZR (up x)) with (x + (IZR (up x) - x))%R.
-  apply Rplus_lt_compat_l; trivial.
-  unfold Rminus in |- *.
-    rewrite (Rplus_comm (IZR (up x)) (- x)) in |- *.
-    rewrite <- Rplus_assoc in |- *.
-    rewrite Rplus_opp_r in |- *.
-    apply Rplus_0_l.
- elim H0.
-   unfold Rminus in |- *.
-   rewrite (Rplus_comm (IZR (up x)) (- x)) in |- *.
-   rewrite <- Rplus_assoc in |- *.
-   rewrite Rplus_opp_r in |- *.
-   rewrite Rplus_0_l in |- *; trivial.
-Qed.
-
-Notation Rset := (Eqsth R).
-Notation Rext := (Eq_ext Rplus Rmult Ropp).
-
-Lemma Rlt_0_2 : 0 < 2.
-apply Rlt_trans with (0 + 1).
- apply Rlt_n_Sn.
- rewrite Rplus_comm in |- *.
-   apply Rplus_lt_compat_l.
-    replace 1 with (0 + 1).
-  apply Rlt_n_Sn.
-  apply Rplus_0_l.
-Qed.
-
-Lemma Rgen_phiPOS : forall x, InitialRing.gen_phiPOS1 1 Rplus Rmult x > 0.
-unfold Rgt in |- *.
-induction x; simpl in |- *; intros.
- apply Rlt_trans with (1 + 0).
-  rewrite Rplus_comm in |- *.
-    apply Rlt_n_Sn.
-  apply Rplus_lt_compat_l.
-    rewrite <- (Rmul_0_l Rset Rext RTheory 2) in |- *.
-    rewrite Rmult_comm in |- *.
-    apply Rmult_lt_compat_l.
-   apply Rlt_0_2.
-   trivial.
- rewrite <- (Rmul_0_l Rset Rext RTheory 2) in |- *.
-   rewrite Rmult_comm in |- *.
-   apply Rmult_lt_compat_l.
-  apply Rlt_0_2.
-  trivial.
-  replace 1 with (0 + 1).
-  apply Rlt_n_Sn.
-  apply Rplus_0_l.
-Qed.
-
-
-Lemma Rgen_phiPOS_not_0 :
-  forall x, InitialRing.gen_phiPOS1 1 Rplus Rmult x <> 0.
-red in |- *; intros.
-specialize (Rgen_phiPOS x).
-rewrite H in |- *; intro.
-apply (Rlt_asym 0 0); trivial.
-Qed.
-
-Lemma Zeq_bool_complete : forall x y, 
-  InitialRing.gen_phiZ 0%R 1%R Rplus Rmult Ropp x =
-  InitialRing.gen_phiZ 0%R 1%R Rplus Rmult Ropp y ->
-  Zeq_bool x y = true.
-Proof gen_phiZ_complete Rset Rext Rfield Rgen_phiPOS_not_0.
-
-Lemma Rdef_pow_add : forall (x:R) (n m:nat), pow x  (n + m) = pow x n * pow x m.
-Proof.
-  intros x n; elim n; simpl in |- *; auto with real.
-  intros n0 H' m; rewrite H'; auto with real.
-Qed.
-
-Lemma R_power_theory : power_theory 1%R Rmult (eq (A:=R))  nat_of_N pow.
-Proof.
- constructor. destruct n. reflexivity.
- simpl. induction p;simpl. 
- rewrite ZL6. rewrite Rdef_pow_add;rewrite IHp. reflexivity.
- unfold nat_of_P;simpl;rewrite ZL6;rewrite Rdef_pow_add;rewrite IHp;trivial.
- rewrite Rmult_comm;apply Rmult_1_l.
-Qed.
-
-Ltac Rpow_tac t := 
-  match isnatcst t with
-  | false => constr:(InitialRing.NotConstant)
-  | _ => constr:(N_of_nat t)
-  end. 
-
-Add Field RField : Rfield  
-   (completeness Zeq_bool_complete, power_tac R_power_theory [Rpow_tac]).
-
-
-
-