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Extend the theory of the positive rationals `Qp`.
- Remove the coercion from `Qp` to `Qc`, and remove it into from `Qp_car` into `Qp_to_Qc` to be consistent with other conversion functions. - Use `let '(..) = ...` in the definitions of `Qp_plus`/`Qp_mult`/`Qp_div` to avoid Coq tactics (like `injection`) to unfold these definitions eagerly. - Define orders `Qp_le` and `Qp_lt`, instead of relying on the orders on `Qc`, which were obtained through the removed coercion into `Qc`. - Lift lemmas about the orders from `Qc` to `Qp`. - Improve variable names and use of notation scopes.
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