Sentence examples for simple proof for from inspiring English sources

Here, we present a simple proof for this fact.

Next, we give a simple proof for Theorem 1.3.

Here we give a simple proof for the reader's convenience.

In Theorem 3.1, we give a simple proof for this case.

The corollary of this gives a correct and simple proof for the result in [8].

We also formulate a simple proof for the averaging formula for the Lefschetz coincidence number.

By using the transfer theorem, we obtain simple proofs for some well-known results (Theorems 2 and 3) and new stability conditions (Theorems 4 and 5) for the Levin-Nohel equations.

Furthermore, in [15] it has been shown that using this relationship one can provide insightful and simple proofs for multiuser single antenna problems such as the broadcast channel and the secrecy capacity problem.

In 1972, Hedberg [9] gave a simpler proof for all α.

A simpler proof for the special case of 2-players and 2-channels is given in [32].

(For a simple proof of Theorem 1, except for a strict rather than a weak preference relation, consult Peterson 2009: 95).