As may be proved; demonstrably.

By logical or practical demonstration; (also) in a way that establishes the truth or existence of something; conclusively.

By means of demonstrative reasoning; so as to produce or provide axiomatic or certain knowledge; conclusively. Cf. scientifical, adj. 1, scientific…

In a declarative manner, by way of declaration or distinct assertion; †by way of manifestation.

In a way that can be proved or made evident; (also) in a way that is evident; to a clearly apparent extent; manifestly.

In a way capable of being affirmed; demonstrably.

by way of probation or of proof.

In a proven manner.