Library Coq.QArith.Qcanon
Qc : A canonical representation of rational numbers.
based on the setoid representation Q.
An alternative statement of Qred q = q via Z.gcd
Coercion from Qc to Q and equality
Q2Qc : a conversion from Q to Qc.
equality on Qc is decidable:
The addition, multiplication and opposite are defined
in the straightforward way:
0 and 1 are apart
Addition is associative:
0 is a neutral element for addition:
Commutativity of addition:
Properties of Qopp
Multiplication is associative:
0 is absorbing for multiplication:
1 is a neutral element for multiplication:
Commutativity of multiplication
Distributivity
Integrality
Inverse and division.
Properties of order upon Qc.
Large = strict or equal
x<y iff ~(y<=x)
Some decidability results about orders.
Compatibility of operations with respect to order.
Rational to the n-th power
And now everything is easier concerning tactics:
A ring tactic for rational numbers
A field tactic for rational numbers