One definition of "demonstration"
From Gerard Sfez, "Demonstration (French: Manifestation, German: Kundgebung, Manifestation)," in Dictionaire critique du marxisme, edited by Georges Labica and Gérard Bensussan (Paris: Presses Universitaires de France, 1999), pp. 691-692:
"At the intersection of the registers of the 'theory of knowledge' and political practice, this term has long signified a religious model of truth, understood as being revealed, incarnated. Close to such notions as appearance and apparition (Schein-Erscheinung), demonstration was the indication of a truth and only that. Kant and especially Hegel were to make of it a moment in the process of the constitution of truth, 'an essential moment of essence,' a moment entering into its concrete determination.(Translated by Ted Stolze.)
Historical materialism has especially revived this term in order to exhibit its double status. Thus, religion is at the same time the demonstration of real misery and a protest against it. This double status of demonstration that calls it a negative determination is of course very marked by Hegel.
Later, the term demonstration in the political field designates more than the function of an indication; it designates a function of anticipation and of constitution of the balance of forces. A demonstration creates a balance of forces rather than repeating or reflecting one; it possesses a formative energy in the dynamic of history. A religious functioning of the demonstration defuses it in order to make it function as a juridical regulation of the system and of the ruling State. The right to demonstrate thus constitutes for Lenin an element that is necessary for this dynamic whose principal function is to shatter the very element of Law."