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.
Note that Theorem 4.2 proves the convergence to a fixed point in, with being constructively proven to be nonempty by first building a sufficiently large convex compact so that the solution of the iterative scheme (4.1) is always bounded on.
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.
We constructively prove the existence and uniqueness of rational-order power functions, which enables us to present graphs of power functions on some chosen time scales for the first time.
In particular, in proving game-theoretic properties like fairness, we demonstrate success for the specific strategy that the protocol designer had in mind, instead of non-constructively proving that a strategy exists.
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.
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.
The upper bounds are proven constructively for approximation and non-constructively for integration.
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.
