Very sure, certain, secure, or confident.

Having fixed or exact limits; clearly defined, determinate, fixed, certain; exact, precise. (Of material, or, more commonly, immaterial things.)

Well-ascertained, certain, sure. Of an argument: Well-founded, valid. Obsolete.

esp. Of a belief, sentiment, hypothesis, etc.: based on good evidence or reasons; having a foundation in fact or reality.

Acknowledged without doubt to be true or to be the thing specified; unquestionable, irrefutable. Obsolete.

Conclusively and reliably shown to be true or certain; demonstrably proved to be the case.

Chiefly U.S. Of an extremely strict or rigorous character; unable to be changed, evaded, or resisted; firm, inflexible. Cf. cast iron, n. 2b.

Chiefly U.S. Firmly grounded, honest, sound; (also) fundamental, basic.