Sentence examples for implies the proposition from inspiring English sources

This implies the proposition by Corollary 1. □ Now imagine that x and z are two MANs, and y is on the path between x and z.

A last type of inference is called contraposition and is produced by the fact that some propositions imply the proposition that results from the original proposition when both of its term variables are negated and their order reversed.

Assume that consists of those maximaLemmaching with an identical weight.

(4.25) Then the above analysis implies the following proposition.

For a set-valued mapping, the convexity implies the quasi-convexity (Proposition 3.9 in [13]).

The last inequality implies the validity of the proposition.

This fact implies the truth of the proposition.

If k is a natural number such that (kimplies the statement of the proposition.

Proposition 5.2 implied the following propositions.

These assumptions are central to the proofs of Theorems 2 and 4. They imply the following proposition stating that the system of stochastic differential equations (Equation 19) is well-posed: Proposition 1 Let T > 0 be a fixed time.

A sentence $A$ implies that the proposition expressed by $B$ is cancelled iff the proposition expressed by $(A \rightarrow B)$ is annihilated.