Federal law permits the prosecution of such witnesses if their crimes can be independently proved.

The conjecture was first proved independently by and .

These results were proved independently by and .

These conjectures were proved independently by and by .

It was independently proved by Marcel Schützenberger, but his contribution escaped notice for several years.

Applying the induction rule repeatedly, starting from the independently proved base case, proves many, often infinitely many, other cases.

The theorem was proved independently by Fáry in 1949 and Milnor in 1950.

Évariste Galois independently proved the theorem in a work that was posthumously published in 1846.

According to other sources, Bolyai and Gerwien had independently proved the theorem in 1833 and 1835, respectively.

The inequality in the above form was proved independently by Kullback, Csiszár, and Kemperman.