Sentence examples for proof is contained from inspiring English sources

The proof is contained in Sect.

As for gradient oscillations, we instead have the following result, whose proof is contained in Sect.

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].

All proofs are contained in Section "Proofs".

All proofs are contained in the appendix.

The main theorems and their proofs are contained in Section 3.

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

However, Proposition 1 suggests that when it exists, the unique equilibrium price breaks down into two possible cases, depending on the relative magnitude of p ⁎ and ε ̲. (Throughout the paper, all omitted proofs are contained in Appendix C).

Proof The equivalence is contained in Proposition 3.7 in [1].

First, consider a game that provides, given an AF F = (A, R ) and argument a ∈ A, a proof whether a is contained in the grounded extension of F. The game is given by the following rules of allowed moves of each player.

The proof of Theorem 1 is contained in Sect.