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Multi-wavelength surveys of solar-like stars have revealed the likely existence of relationships between their rotation, X-ray luminosity, mass-losses and magnetism. Those impose strong constraints on the corona and wind of cool stars.\n  Aims. We aim to provide power-law prescriptions of the mass-loss of stars, of their magnetic field, and of their base coronal density and temperature that are compatible with their observationally-constrained spin-down.\n  Methods. 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