Sentence examples for contained in the proof of from inspiring English sources

The proof is contained in the proof of Theorem 3. We have stated that for all utility function K-tuples u − k ∈ U K − 1 and for all utility functions uk ≠ 0 and for an arbitrarily chosen user j ∈ K ∖ k, we have that inf r ∈ Q k ( u − k ) r k = inf u k ≠ 0 f k ( ( u k, u − k ) ) > 0. Theorem 4 has a certain connection to the axiom non-dummy introduced in[18].

Stevenson's text includes nine poems contained in the 1883 trial proof of Child's Garden but excluded from subsequent published editions.

The idea of the proof of the next lemma is contained in the paper of Fang and Huang [10].

The proof as to what then took place is contained in the testimony of three witnesses.

Geometrical knowledge typically concerns two kinds of things: theoretical or abstract knowledge contained in the definitions, theorems, and proofs in a system of geometry; and some knowledge of the external world, such as is expressed in terms taken from a system of geometry.

Axioms are simply the assumptions of the proofs contained in the physical theory.

The last section contains the proof of the main result.

Section 3 contains the proof of our main result.

A document containing the proof of this for the LOCF case, with a full derivation of the standard error, is available in the Supporting information.

The proof of Proposition 3.3 is contained in the following.

For the ease of readability, all proofs are contained in the Appendix.