Sentence examples for various proof from inspiring English sources

These include the systematic design of semantics modeling various proof methods and the characterization of assertions as abstract domains.

These games are a useful device for showing upper and lower bounds on the lengths of proofs in various proof systems.

In collating, you used a pencil to carefully transfer changes from various proofs from the editor, the author, the proofreaders (usually two), the lawyer, and the fact checker onto a clean proof for the printer.

The exponential inequality plays an important role in various proofs of limit theorems.

Le Grand responded to Parker's charges of atheism in his Apologia de Descartes (1679), challenging Parker's criticisms with various proofs of God's existence.

It is well known that the probability inequality plays an important role in various proofs of limit theorems.

Since the appearance of this inequality various proofs and generalizations or improvements have appeared in the literature for different types of differential equations.

In the subsequent papers, various proofs and reformulations of this inequality have been presented, we refer to [2, Chapter XIII], and to [3 5] for some details.

The exponential inequality for the partial sums ∑ i = 1 n ( X i − E X i ) plays an important role in various proofs of limit theorems.

An expansion proof is a generalization of the notion of a Herbrand expansion of a theorem of first-order logic; it provides a very elegant, concise, and nonredundant representation of the relationship between the theorem and a tautology which can be obtained from it by appropriate instantiations of quantifiers and which underlies various proofs of the theorem.

The exponent α M is in general strictly less than one (see again [67]); while lower bounds on α M can be obtained by tracking the constant dependence in the various proofs, its precise (optimal) value is not known.