Sentence examples for proof with a from inspiring English sources

We complete the proof with a series of statements below.

Then the above proof with a minor modification also leads to a contradiction.

We start the proof with a lemma which provides appropriate conditions in order to apply a fixed point theorem.

To make the article as self-contained as possible, we will give a simple proof with a slight modification to [8].

Some ready framed items which might make perfect Christmas gifts include a VIP Spectre poster estimated at $800 to $920£60000 to £700) and an Indiana Jones Drew Struzan artist's proof with a guide price of $400 to $530£30000 to £400).

The highest value listed is for the 1877, struck only in proof with a mintage of 900, at $2,000.

Root is strong (80 proof), with an earthy, herbal, lightly citric flavor, at once bitter from birch bark, yet kissed with the rummy sweetness of its organic sugar cane distillate.

It's also kid-proof, with a toughened screen, rubberised case and a two-year guarantee.

The investigators found that the process was nearly fail-proof, with a 96percentt success rate, and attributed these outcomes to the young age at which they initiated intervention.

Ivan's was, well, bare-bones: The cabins were relatively mosquito-proof, with a single electric fan to keep us cool; the toilets and showers, outside amid coconut palms and tamarind trees, didn't clog until Saturday.

A manual transmission without a clutch pedal, it makes lightning upshifts and silky downshifts almost idiot-proof, with a literal flick of the wrist to paddles behind the steering wheel.