then the proof

USAGE SUMMARY

The phrase "then the proof" is correct and usable in written English.
It can be used when transitioning to a demonstration or verification of a statement or argument previously made. Example: "We have established the theory; now, then the proof will illustrate its validity."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

60 human-written examples

Then the proof is completed.

Pacific Journal of Mathematics for Industry

Denote ; then the proof is complete.

Boundary Value Problems

Then the proof is completed easily.

Advances in Difference Equations

If, then the proof is finished.

Fixed Point Theory and Applications

Then, the proof of sufficient is complete.

Boundary Value Problems

Then the proof can be completed easily.

Advances in Difference Equations

If, then the proof is analogous.

Advances in Difference Equations

If, then the proof is complete.

Advances in Difference Equations

Then, the proof of (19) is presented.

EURASIP Journal on Advances in Signal Processing

Then the proof follows from Corollary 18. □.

Journal of Inequalities and Applications

end{aligned} Then the proof is completed.

Boundary Value Problems

Expert writing Tips

Best practice

Use "then the proof" to clearly signal the transition from stating a proposition to demonstrating its validity in a logical or mathematical argument.

Common error

Avoid using "then the proof" in contexts where a formal demonstration or logical deduction isn't actually present. Overusing it in informal conversation can sound pretentious or out of place.

Linguistic Context

The phrase "then the proof" functions as a transitional phrase, indicating the commencement of a demonstration or verification, typically in a mathematical or logical context. As confirmed by Ludwig, the phrase is correct and signals a shift in the argument.

Expression frequency: Very common

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Ludwig's WRAP-UP

In summary, the phrase "then the proof" serves as a transitional marker, explicitly signaling the commencement of a logical or mathematical demonstration. Ludwig AI confirms its grammatical correctness and suitability for transitioning into the proof or verification phase. Primarily observed in scientific and academic contexts, its function is to provide justification or validation for previously stated claims. While perfectly acceptable, more informal alternatives like "therefore" or "thus" might be considered for broader audiences. The usage is very common in scientific literature.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

hence the demonstration

Replaces "proof" with "demonstration" for a slightly more formal tone.

thus the verification

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

therefore the confirmation

Uses "confirmation" instead of "proof" to highlight the establishment of validity.

consequently the validation

Replaces "proof" with "validation", focusing on the act of proving something's accuracy.

as a result the evidence

Changes the structure to emphasize the evidentiary nature of the argument.

it follows that the argument

Shifts the focus to the logical consequence leading to the argument's validity.

in consequence the justification

Replaces "proof" with "justification", highlighting the reasoning behind the conclusion.

subsequently the reasoning

Focuses on the sequential nature of the argument's logic.

in that case the demonstration

Introduces a conditional element to the phrase, emphasizing the specific circumstance.

by implication the confirmation

Highlights the indirect but logical connection to the confirmed result.

FAQs

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

You can use "then the proof" to signal the start of a logical demonstration following a statement, such as, "We've established the conditions; "then the proof" will show its validity".

What is a more common alternative to "then the proof"?

While "then the proof" is correct, alternatives like "therefore", "thus", or "consequently" can often serve the same purpose with a less formal tone.

In what contexts is "then the proof" most appropriate?

"Then the proof" is particularly suited for academic papers, mathematical derivations, and formal logical arguments, particularly in science or mathematics.

Is there a difference between saying "then the proof is complete" versus "then the proof is completed"?

Both phrases are grammatically correct. "Then the proof is complete" implies a state of being finished, while "then the proof is completed" emphasizes the action of finishing. The choice depends on the desired emphasis.