hence the proof

USAGE SUMMARY

'hence the proof' is correct and usable in written English.
It is typically used to indicate that something has been explained or demonstrated previously, and that it is now supported with evidence. For example, "The theorem has been explored in detail, and hence the proof is solid."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

60 human-written examples

Hence, the proof follows.

Advances in Difference Equations

Hence the proof.

Complex & Intelligent Systems

Hence the proof is completed.

Journal of Inequalities and Applications

Hence the proof is over.

Advances in Difference Equations

Hence the proof is finished.

Journal of Inequalities and Applications

Hence the proof is done.

Boundary Value Problems

Hence the proof is omitted.

Journal of Inequalities and Applications

thus and Hence, The proof is complete.

Advances in Difference Equations

end{cases} Hence, the proof is complete.

Advances in Difference Equations

Hence the proof of our results follows.

Advances in Difference Equations

Hence the proof of (3.3) is completed.

Journal of Inequalities and Applications

Expert writing Tips

Best practice

When using "hence the proof", ensure that the preceding text provides sufficient justification and evidence for the statement being proven.

Common error

Avoid using "hence the proof" if the preceding steps or arguments are unclear or incomplete. Ensure that all necessary assumptions and logical steps are explicitly stated before concluding with this phrase.

Linguistic Context

The phrase "hence the proof" serves as a conjunctive adverbial phrase, signaling the conclusion of a logical argument or mathematical derivation. It functions to explicitly state that what precedes it provides sufficient evidence to validate the assertion, as supported by Ludwig AI.

Expression frequency: Very common

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Encyclopedias

0%

Ludwig's WRAP-UP

The phrase "hence the proof" is a grammatically correct and commonly used expression, especially in scientific and academic writing. Ludwig AI indicates that it is used to signify the conclusion of a logical argument or mathematical demonstration. The phrase's function is to formally state that what precedes it sufficiently validates the assertion. Given its prevalence in scientific contexts, its register is decidedly formal and scientific. To enhance clarity, ensure that preceding arguments are complete before employing this phrase. While "hence the proof" is correct, alternatives like "thus the demonstration" or "therefore the evidence" can be used to vary your writing style.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

thus the demonstration

Replaces "proof" with "demonstration", focusing on the act of showing something to be true.

therefore the evidence

Uses "evidence" instead of "proof", shifting the focus to the supporting information.

consequently the verification

Substitutes "proof" with "verification", emphasizing the act of confirming the truth.

as a result the confirmation

Replaces "hence" with "as a result" and "proof" with "confirmation", highlighting the outcome.

accordingly the validation

Uses "accordingly" and "validation" to provide a more formal tone while maintaining the original meaning.

in consequence the substantiation

Replaces "hence" and "proof" with more formal synonyms, increasing the complexity.

it follows that the proof is complete

Expands the original phrase to explicitly state the completion of the proof.

the demonstration is thus concluded

Rephrases the idea to emphasize the conclusion of the demonstration.

the evidence leads to this conclusion

Focuses on the evidence and its role in reaching the conclusion.

this confirms the result

Simplifies the statement to directly confirm the result based on prior information.

FAQs

How can I use "hence the proof" in a sentence?

"Hence the proof" is typically used at the end of a logical argument or mathematical derivation to indicate that the preceding steps have successfully demonstrated the claim.

What are some alternatives to "hence the proof"?

Alternatives include phrases like "thus the demonstration", "therefore the evidence", or "consequently the verification". You can also use "it follows that" or "this proves that".

Is "hence the proof" appropriate for informal writing?

While grammatically correct, "hence the proof" is more suitable for formal or academic writing. In informal contexts, simpler alternatives might be preferred.

What is the difference between "hence the proof" and "therefore, the proof"?

"Hence the proof" is a more concise and formal way of saying "therefore, the proof". Both indicate that the preceding information leads to the conclusion, but "hence" is often preferred in mathematical or logical arguments for its brevity.