[1] His parents Jan W. Trybulec and Barbara H. Kurlus both were professional pharmacists who owned a chemists shop in a small town Szczucin near the city of Tarnów in the south-eastern Poland where they dispensed medicines.

In September and October 1973, Trybulec was a visiting professor to the All-Russian Scientific and Technical Information Institute (VINITI) in Moscow, then the USSR, where he invented the idea of machine-readability of a mathematical text.

Trybulec's first mathematical papers were in the various topological and metric space topics pioneered by Karol Borsuk.

In parallel to his generic topological research, he also worked in computational linguistics and semantics of programming languages.

Applying the framework of Tarski–Grothendieck set theory axioms, essentially the Zermelo–Fraenkel set theory supplemented by the Tarski axiom with all the objects being sets and eliminated notion of class, together with the first-order logic of the Gentzen-Jaśkowski natural deduction, in 1973 he designed the formalization system Mizar consisting of a formal language for writing mathematical definitions and proofs, a proof assistant, able to mechanically check proofs written in this language.