Sentence examples for follows proof from inspiring English sources

Proof It follows proof similar to the proof of Lemma 1 of Kiany andAmini-Harandi [22].

Our proofs of this theorem closely follows proofs given in [11] for some related results.

People have indeed followed proofs in these systems.

The rest of the proof follows the proof of Theorem 3.6 and then we apply Corollary 2.7.

Proof Following the proof of Theorem 1, FS ≠ ∅.

Proof Following the proof of Theorem 1, FT ≠ ∅.

Proof Following the proof of Theorem 2.1, there exists y ∈ X such that lim k → ∞ b d ( y k, y ) = 0. (2.24).

Proof Following the proof of Theorem 3.1, T and g have a unique coupled common fixed point ( x, y ).

The proof given there structurally closely follows the proof of the original PCP theorem by Dinur (2007).

Our diagrammatic proof of the dominance theorem follows the proof of Arrow's possibility theorem in [ 29].

Now the proof follows as the proof of Theorem 4.1.