Sentence examples for proofs follow from inspiring English sources

Third, the proofs follow the design intuition.

The proofs follow from oscillation theory and boundedness of the boundary conditions.

The rest of the proofs follow from part (a), and this concludes the proof.

The proofs follow from the study of the Dirichlet problem (1.1) with and.

We now prove the correctness of Eq. 18, the other ones' proofs follow the same line.

Theorems 6.1 and 6.3 are improved versions of Theorems 1 and 2 from [1], and their proofs follow the lines of those given therein.

The proof follows from the following equalities: (2.17).

Hence, the proof follows.

Proof follows from (i).

Proof Following the steps of Theorem 2.3, proof follows immediately.

The proof follows from (3.12).