diff options
Diffstat (limited to 'theories/Reals/Rdefinitions.v')
| -rw-r--r-- | theories/Reals/Rdefinitions.v | 58 |
1 files changed, 29 insertions, 29 deletions
diff --git a/theories/Reals/Rdefinitions.v b/theories/Reals/Rdefinitions.v index 75a082cfce..a862a0ac39 100644 --- a/theories/Reals/Rdefinitions.v +++ b/theories/Reals/Rdefinitions.v @@ -15,55 +15,55 @@ Require Export ZArith_base. -Parameter R:Set. +Parameter R : Set. (* Declare Scope positive_scope with Key R *) -Delimits Scope R_scope with R. +Delimit 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. +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. +Infix "+" := Rplus : R_scope. +Infix "*" := Rmult : R_scope. +Notation "- x" := (Ropp x) : R_scope. +Notation "/ x" := (Rinv x) : R_scope. -V8Infix "<" Rlt : R_scope. +Infix "<" := Rlt : R_scope. (*i*******************************************************i*) (**********) -Definition Rgt:R->R->Prop:=[r1,r2:R](Rlt r2 r1). +Definition Rgt (r1 r2:R) : Prop := (r2 < r1)%R. (**********) -Definition Rle:R->R->Prop:=[r1,r2:R]((Rlt r1 r2)\/(r1==r2)). +Definition Rle (r1 r2:R) : Prop := (r1 < r2)%R \/ r1 = r2. (**********) -Definition Rge:R->R->Prop:=[r1,r2:R]((Rgt r1 r2)\/(r1==r2)). +Definition Rge (r1 r2:R) : Prop := Rgt r1 r2 \/ r1 = r2. (**********) -Definition Rminus:R->R->R:=[r1,r2:R](Rplus r1 (Ropp r2)). +Definition Rminus (r1 r2:R) : R := (r1 + - r2)%R. (**********) -Definition Rdiv:R->R->R:=[r1,r2:R](Rmult r1 (Rinv r2)). +Definition Rdiv (r1 r2:R) : R := (r1 * / r2)%R. -V8Infix "-" Rminus : R_scope. -V8Infix "/" Rdiv : R_scope. +Infix "-" := Rminus : R_scope. +Infix "/" := Rdiv : R_scope. -V8Infix "<=" Rle : R_scope. -V8Infix ">=" Rge : R_scope. -V8Infix ">" Rgt : R_scope. +Infix "<=" := Rle : R_scope. +Infix ">=" := Rge : R_scope. +Infix ">" := 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. +Notation "x <= y <= z" := ((x <= y)%R /\ (y <= z)%R) : R_scope. +Notation "x <= y < z" := ((x <= y)%R /\ (y < z)%R) : R_scope. +Notation "x < y < z" := ((x < y)%R /\ (y < z)%R) : R_scope. +Notation "x < y <= z" := ((x < y)%R /\ (y <= z)%R) : R_scope.
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