Sentence examples for proven statements from inspiring English sources

Although it's nice to imagine the Olympics as a beacon of peace and equality in a world rife with discrimination, the history of the Games has proven statements like these to be problematic and hollow.

Similarly, one can prove statements (d) and (e).

So we have proved statements (1) and (2).

We shall prove statements by induction on N. If ({N = 0}), then (4.10) holds trivially.

(2) When formulating and proving statements, we understand that (2) is valid without mentioning this property.

Frege's system (i.e., his term logic/predicate calculus) consisted of a language and an apparatus for proving statements.

We introduce a reasoning infrastructure for proving statements about resource consumption in a fragment of the Java Virtual Machine Language (JVML).

The point of the 'game of higher mathematics' consists, in Hilbert's view, in proving statements of elementary arithmetic, which do have a direct interpretation (Hilbert 1925).

So Hilbert and his students set out to prove statements such as the consistency of the standard postulates of mathematical analysis.

Depending on the circumstances of your marriage and divorce, you may have to attach additional documents to your complaint to prove statements you've made in your complaint.

This proves statement (3).