Sentence examples for concise proof from inspiring English sources
Proof We give only a concise proof.
gThis concise proof is based on Uzawa's proof.
Proof We give again only a concise proof.
A concise proof of the First Theorem can also be found in [38].
As we use the eigenvalues in the sequel, we present a concise proof.
In Section 4, we give a concise proof for an L p extension of Theorem 1 of [15].
This allowed us to give concise proofs of type soundness, erasure and simulation theorems.
This section presents concrete mathematical analysis results on unique existence and comparative statics on τ * with concise proofs.
Their formulation and presentation of the trust (lambda )-calculus adopt a small-step semantics and a Church style type system, supporting concise proofs of type soundness, erasure and simulation theorems.
In order to make the proof more concise, we only consider the case of (p< r<2p
Suppose that somebody now comes to you with a huge hypergraph built with axiom, cut, par and tensor links, pretending that it is actually a concise representation of the proof of some long standing open mathematical problem.
