Sentence examples for a separate proof from inspiring English sources

Supplementarily we now give a separate proof without using the topological equivalence of ({d_{L^p}}) and ({e_{L^p}}) specified in Corollary 15 (see [54, Section 5.1] or [53, Section 5.1] for the corresponding metrics on (L^2) with different arguments).

Our study is limited by the fact that many of our predicted miRNA:mRNA interactions remain in silico only, and require a separate proof of regulation on an individual basis for any given interaction.

The systematic derivation of the generalization algorithms from the modal truth criterion obviates the need for carrying out a separate formal proof of correctness of the EBG algorithms.

I keep them in a separate, sound-proof room now, where they can't disturb me.

He has a sewing table, an area to mix paint and resin, a corner office, and a separate, sound-proof room for creating audio work.

Each group was maintained in a separate light-proof room throughout the experiment.

But the Department of Housing and Urban Development, which provides housing vouchers and other crucial services, has required separate proofs that a family with children, or an unaccompanied minor, is actually homeless.

In this sense of conversion, the passage from a proposition to its converse is not, in general, a valid inference; and though often a mathematical proposition and its converse may both hold, separate proofs must be given for each case.

The correct way of dealing with this duality is to provide separate proofs.

One of the defendants, Celotex Corporation, made a separate proffer of proof, indicating that it was the purchaser of a license from a licensee, American Gypsum Company.

Non-systematic or narrative reviews were excluded, but collected as a separate category as proof of existing clinical knowledge/practice.