direct proof
collocation in Englishmeaningsofdirectandproof
These words are often used together. Click on the links below to explore the meanings. Or,see other collocations withproof.
direct
adjective
uk/daɪˈrekt/us/daɪˈrekt/
going in a straight line towards somewhere or someone without stopping or ...
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proof
noun
uk/pruːf/us/pruːf/
a fact or piece of information that shows that something exists or ...
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(Definition ofdirectandprooffrom theCambridge English Dictionary© Cambridge University Press)
Examplesofdirect proof
These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors.
We give adirectproof.
From theCambridge English Corpus
We indicate adirectprooffor completeness.
From theCambridge English Corpus
We give the followingdirectproof.
From theCambridge English Corpus
I do not know anydirectproof.
From theCambridge English Corpus
Here we provide a shorter, moredirectproof.
From theCambridge English Corpus
We shall give adirectproofof the latter result.
From theCambridge English Corpus
We do not know anydirectproofof this proposition.
From theCambridge English Corpus
A simpledirectproofcan be obtained by the following route.
From theCambridge English Corpus
The recursive definition of hextract makes adirectproofof this property difficult.
From theCambridge English Corpus
Adirectproofthat it is a resolution may be quite hard.
From theCambridge English Corpus
In what follows, we give adirectproofof the conjugacy.
From theCambridge English Corpus
However, adirectproofis much easier, and we have not found one in the literature.
From theCambridge English Corpus
We found it simpler to write adirectproofthan to appeal to his generic framework.
From theCambridge English Corpus
In what follows we give an elementarydirectproofbased on a dynamic programming equation.
From theCambridge English Corpus
Nevertheless, it seems quite possible that one can construct adirectproofof these improved results.
From theCambridge English Corpus
We were not able, however, to find adirectproofof this fact.
From theCambridge English Corpus
In the following we give adirectproofof this result.
From theCambridge English Corpus
This allows us to give a clean anddirectproof, dealing simultaneously with all times along each orbit.
From theCambridge English Corpus
Directprooffor an in vivo role of endo- mannanase by sense- and antisense-transformation of tomato is still lacking.
From theCambridge English Corpus
For completeness, and for those who are not familiar with the theory of quasifactors, we provide an alternativedirectproof.
From theCambridge English Corpus
The correctness of this principle and its application in many cases has long been capable ofdirectproof.
From theCambridge English Corpus
We have found a shortdirectprooffor the (2, 1) -choosability of triangle-free outerplanar graphs.
From theCambridge English Corpus
These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors.
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