  We give an analytic (free of computer assistance) proof of the existence of a
classical Lorenz attractor for an open set of parameter values of the Lorenz
model in the form of Yudovich-Morioka-Shimizu. The proof is based on detection
of a homoclinic butterfly with a zero saddle value and rigorous verification of
one of the Shilnikov criteria for the birth of the Lorenz attractor; we also
supply a proof for this criterion. The results are applied in order to give an
analytic proof of the existence of a robust, pseudohyperbolic strange attractor
(the so-called discrete Lorenz attractor) for an open set of parameter values
in a 4-parameter family of three-dimensional Henon-like diffeomorphisms.
