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(***********************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
(* \VV/ *************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(***********************************************************************)
(* $Id$ *)
Require Rbase.
Tactic Definition Sup0 :=
Match Context With
| [ |- (Rgt R1 R0) ] -> Unfold Rgt;Apply Rlt_R0_R1
| [ |- (Rgt (Rplus R1 ?1) R0) ] ->
Apply (Rgt_trans (Rplus R1 ?1) ?1 R0);
[Pattern 1 (Rplus R1 ?1);Rewrite Rplus_sym;Unfold Rgt;
Apply Rlt_r_r_plus_R1
|Sup0].
Tactic Definition DiscrR :=
Match Context With
| [ |- ~R1==R0 ] -> Red;Intro;Apply R1_neq_R0;Assumption
| [ |- ~((Rplus R1 ?1)==R0) ] -> Apply Rgt_not_eq;Sup0
| [ |- ~(Ropp ?1)==R0 ] -> Apply Ropp_neq; DiscrR
| [ |- ~(?1==?1) ] -> ElimType False
| [ |- ~(Rminus R0 ?1)==R0 ] -> Rewrite Rminus_Ropp; DiscrR
| [ |- ~(?1==?2) ] ->
(Apply Rminus_not_eq; Ring (Rminus ?1 ?2);
(Match Context With
| [ |- ~(Rplus (Ropp R1) ?)==R0 ] ->
Repeat Rewrite <-Ropp_distr1; DiscrR
| [ |- ? ] -> DiscrR)
Orelse (Apply Rminus_not_eq_right; DiscrR)).
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