  It is discussed a practical possibility of a provable programming of
mathematics basing on intuitionism and the dependent types feature of a
programming language.The principles of constructive mathematics and provable
programming are illustrated with examples taken from algebra. The discourse
follows the experience in designing in Agda a computer algebra library DoCon-A,
which deals with generic algebraic structures and also provides the needed
machine-checked proofs.
  This paper is a revised translation of a certain paper published in Russian
in 2014.
