Sentence examples for By proposition from inspiring English sources

By Proposition 2.3 no.

By Proposition 3.4, whenever.

By Proposition 2.1, we obtain.

By Proposition 1.20   is -convex.

By Proposition 3.3, we have.

By Proposition 2.5, (LinGamma_{f}).

By Proposition 3.7, we get.

By Proposition 2.2,, and as, being.

By Proposition 2.3 f is X-midconvex.

By Proposition in [8], as for.

By Proposition 3.7, T μ x = Px.