Sentence examples for proof in view of from inspiring English sources

Proof In view of Theorem 1, C ( f, g ) ≠ ∅.

Proof In view of Corollary 3.1, we know that.

This concludes the proof, in view of (2.12).

Proof In view of Lemma 1, equation (7) has three positive roots of multiplicity one.

Proof In view of Lemma 4.2, the identity is obtained by straightforward calculation.

Proof In view of (4.2), we may assume that = ( 0, 1 ).

Proof First, in view of (3.2), we have to prove that m 2 ( 1 − ε κ ) 2 ≥ m 4 + κ ε κ 4 ε κ 2, which is equivalent to κ ≤ m 4 2 ε κ − 1 ε κ 4 ( 1 − ε κ ) 2. By replacing the expression of κ given by (2.9), we obtain 1 ≤ m 4, which implies that (3.5) holds for all m ∈ N.

Let D k denote the determinant of the submatrix of Discr ( f ˜ ), formed by the first 2k rows and the first 2k columns, for k = 1, 2, 3, 4. So, by straightforward calculation one can see that D 1 = 4, D 2 = 4 Δ 1, D 3 = 4 c 2 Δ 2, and D 4 = c 4 Δ 3. The rest of the proof follows in view of [[44], Theorem 1].

Proof The proof is obvious in view of the previous theorem.

The proof is obvious in view of Lemma 2.1.

Proof of Theorem 1.4 In view of the proofs of Theorem 1.2 and Theorem 1.3, the conclusion of Theorem 1.4 holds.