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Diffstat (limited to 'theories7/Reals/Rdefinitions.v')
-rw-r--r-- | theories7/Reals/Rdefinitions.v | 69 |
1 files changed, 0 insertions, 69 deletions
diff --git a/theories7/Reals/Rdefinitions.v b/theories7/Reals/Rdefinitions.v deleted file mode 100644 index 79be0176..00000000 --- a/theories7/Reals/Rdefinitions.v +++ /dev/null @@ -1,69 +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: Rdefinitions.v,v 1.1.2.1 2004/07/16 19:31:34 herbelin Exp $ i*) - - -(*********************************************************) -(** Definitions for the axiomatization *) -(* *) -(*********************************************************) - -Require Export ZArith_base. - -Parameter R:Set. - -(* Declare Scope positive_scope with Key R *) -Delimits Scope R_scope with R. - -(* Automatically open scope R_scope for arguments of type R *) -Bind Scope R_scope with R. - -Parameter R0:R. -Parameter R1:R. -Parameter Rplus:R->R->R. -Parameter Rmult:R->R->R. -Parameter Ropp:R->R. -Parameter Rinv:R->R. -Parameter Rlt:R->R->Prop. -Parameter up:R->Z. - -V8Infix "+" Rplus : R_scope. -V8Infix "*" Rmult : R_scope. -V8Notation "- x" := (Ropp x) : R_scope. -V8Notation "/ x" := (Rinv x) : R_scope. - -V8Infix "<" Rlt : R_scope. - -(*i*******************************************************i*) - -(**********) -Definition Rgt:R->R->Prop:=[r1,r2:R](Rlt r2 r1). - -(**********) -Definition Rle:R->R->Prop:=[r1,r2:R]((Rlt r1 r2)\/(r1==r2)). - -(**********) -Definition Rge:R->R->Prop:=[r1,r2:R]((Rgt r1 r2)\/(r1==r2)). - -(**********) -Definition Rminus:R->R->R:=[r1,r2:R](Rplus r1 (Ropp r2)). - -(**********) -Definition Rdiv:R->R->R:=[r1,r2:R](Rmult r1 (Rinv r2)). - -V8Infix "-" Rminus : R_scope. -V8Infix "/" Rdiv : R_scope. - -V8Infix "<=" Rle : R_scope. -V8Infix ">=" Rge : R_scope. -V8Infix ">" Rgt : R_scope. - -V8Notation "x <= y <= z" := (Rle x y)/\(Rle y z) : R_scope. -V8Notation "x <= y < z" := (Rle x y)/\(Rlt y z) : R_scope. -V8Notation "x < y < z" := (Rlt x y)/\(Rlt y z) : R_scope. -V8Notation "x < y <= z" := (Rlt x y)/\(Rle y z) : R_scope. |