Sentence examples for proofs are based on from inspiring English sources
Proofs of Theorems 1.1 and 1.2 The proofs are based on the ideas in [25], but we give the details of the argument for the reader's convenience.
The proofs are based on familiar methods of calculus.
The proofs are based on the crucial inequality (GK).
Our proofs are based on a blocking technique and a stable convergence theorem for semimartingales.
Instead, his two proofs are based on Aristotle's theory of motion, which presents a novelty in medieval Jewish thought.
The proofs are based on new a priori estimates in conormal spaces.
The technique of the proofs is based on construction of appropriate Lyapunov functions.
The proof is based on the concept of types extended to one parameter family of points.
Their proof was based on a neat formula for the payoffs achieved if both players use memory-one strategies.
British proof is based on a specific concentration of alcohol, a 50 percent alcoholic content being equivalent to 114.12 U.S. proof.
The proof is based on Lemma 1.
