# Smooth implies ... theorem

Let $X$, $Y$ be schemes, and possibly some arrows, satisfying the following conditions:

• $f$ smooth
Then
• $f$ formally smooth, locally of finite presentation, flat

## References

• Stacks Project, https://stacks.math.columbia.edu/tag/02H6 (Fabio)
• Stacks Project, https://stacks.math.columbia.edu/tag/01VF (Fabio)