Sentence examples for a concise proof of from inspiring English sources

A concise proof of the First Theorem can also be found in [38].

In the following, we will give a concise proof for the multiplicity of T-periodic solutions independent of Theorem 4.2.

In Section 4, we give a concise proof for an L p extension of Theorem 1 of [15].

We present a concise proof that the deviation of the actual state from the target state is decaying exponentially with time if a certain control is applied to the nonlinear system.

A better and concise proof of a fundamental proposition concerning the refracted flux across a bi-material interface in the conductivity problem is also provided.

Chapters 3 and 3* of Sen's more general account [ 37] provide a concise proof Arrow's original "General (Im Possibility Theorem" of 1963 - the version that is relevant here.

To provide a concise proof, the following brief graph-theoretical summary of the problem defined in Definition 1 is used.

Proof We give only a concise proof.

Proof We give again only a concise proof.

As we use the eigenvalues in the sequel, we present a concise proof.

This allowed us to give concise proofs of type soundness, erasure and simulation theorems.