Sentence examples for a simple proof for from inspiring English sources

As an application, we give a simple proof for the denseness of the Schwartz class in such spaces.

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

Here, we present a simple proof for this fact.

Next, we give a simple proof for Theorem 1.3.

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

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

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).

Metcalfe and Sogge [24] give a simple proof of global existence for quadratic quasilinear Dirichlet-wave equations outside of a wide class of compact obstacles in the critical case where the spatial dimension is three.

Triple-wise value-restriction suffices for transitive majority preferences (for a simple proof of Sen's theorem, see Elsholtz and List 2005).