Sentence examples for prove constructively from inspiring English sources

We define the median stable matching for two-sided matching markets with wages and prove constructively that it exists.

In the present article we prove constructively the existence of type II blow-up solutions for the Joseph Lundgren critical case, thus giving an answer to this question.

We prove constructively that for any propositional formula $\phi$ in Conjunctive Normal Form, we can either find a satisfying assignment of true and false to its variables, or a refutation of $\phi$ showing that it is unsatisfiable.

In this section, we prove constructively that for odd k there exists an RC complete sequence that achieves the lower bound of Proposition 1 and is thus optimal.

The upper bounds are proven constructively for approximation and non-constructively for integration.

In consequence of this fact, a theorem about sets proved constructively was immediately seen to be valid not only for sets but also for sheaves, which, however, lie beyond the scope of this article.

First, with the aid of properties of the mechanical parameters of two-link planar robots, this paper proves constructively that stable controllers exist for stabilizing the UEP (Upright Equilibrium Point with two links being still in the upright position) of each robot by designing a single output with an adjustable parameter.

Many results in functional analysis have natural point-free proofs (Johnstone 1982, Picardo and Pultr 2011); some of them for instance, the Riesz representation theorem (Coquand and Spitters 2009)—can also be proved completely constructively.

Proof We prove this assertion constructively.

In fact, it seems reasonable to expect that if we constructively prove a disjunction φ∨ψ, then we should also be able to prove φ or prove ψ.

According to Farouki [2], the Bernstein polynomial basis was introduced 100 years ago (Bernstein, 1912) as a means to constructively prove the ability of polynomials to approximate any continuous function, to any desired accuracy, over a prescribed interval.