We define the notion of formal proof sketch for the mathematical language Mizar. We show by examples that formal proof sketches are very close to informal mathematical proofs. We discuss some ways in which formal proof sketches might be used to improve mathematical proof assistants.

: 1, if n = 1, 0, if p|n for some prime p, (−1), if n = p1p2 · · · pr, where pi are distinct primes. as e.g., its multiplicativity. To enable smooth reasoning about the sum of this number-theoretic function, we introduced an underlying many-sorted set indexed by the set of natural numbers. Its elements are just values of the Möbius function. The second part of the paper is devoted to the notion...

Herbal medicines include a range of pharmacologically active compounds: in some cases it is not well understood which ingredients are important for a therapeutic effect. The supporters of herbal medicine believe that isolated ingredients in the majority of cases have weaker clinical effects than whole plant extract, a claim that would obviously require proof in each case. Although a multitude o...