based on this proof

USAGE SUMMARY

"based on this proof" is a perfectly acceptable phrase in written English.
You can use it when you are discussing evidence or an argument, typically after presenting some proof. For example, "Based on this proof, it is my belief that the defendant is guilty."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

3 human-written examples

Based on this proof, we know that equality in (36) holds if and only if (P') is the midpoint of the closed straight line segment ([AA_]).

Journal of Inequalities and Applications

Based on this proof, we know that the equality in (12) holds if and only if Γ is a circle and P is the center of the circle.

Journal of Inequalities and Applications

Based on this proof, we see that the equality in (21) holds if and only if angle A_{i-1}A_{i}A_{i+1}=frac{N-2}{N}pi, quad i=1,2,ldots,N.

Journal of Inequalities and Applications

Human-verified similar examples from authoritative sources

Similar Expressions

57 human-written examples

Based on this proof-of-concept preliminary study, we recommend long-term follow-up of patients enrolled in clinical trials to ascertain a more comprehensive assessment of the efficacy of experimental treatments.

BMC Nephrology

Based on this proof-of principle experiment by MALDI-MS, we are currently performing a large-scale comparative quantitative glycomics experiment utilizing DRAG to identify glycan specific differences in the urinary glycome for various diseases.

Analytical Chemistry

Based on this preliminary proof-of-concept study, we recommend that long-term follow-up be incorporated into the study design of all clinical trials in nephrology that include pediatric and/or adult patients in order to enable more comprehensive assessment of the effect of the experimental treatments under evaluation (word count: 2301).

BMC Nephrology

In Lemma 2.3, based on the proof line from [53], we make a generalization of this inequality.

Advances in Difference Equations

Because the proposed algorithm has a similar strategy of backtracking which is used in ASP, the proofs are mainly based on the proof framework of ASP/ACoSaMP.

EURASIP Journal on Advances in Signal Processing

Based on the proof of Theorem 6.1, we can develop parallel results to Theorems 3.3-3.11 as follows.

Advances in Difference Equations

Future studies, based on the proof of concept provided here, can explore that question productively for the entire first post-transplant year.

Plosone

Based on the proof of Theorem 1, the base of the log must be greater then C in order to achieve the speed up.

Algorithms for Molecular Biology

Expert writing Tips

Best practice

When using "based on this proof", ensure the proof is clearly presented or referenced beforehand to provide context for the reader.

Common error

Avoid making overly broad generalizations or claims that go beyond what the "based on this proof" actually supports. Stick to conclusions that are directly and logically derived from the proof itself.

Linguistic Context

The phrase "based on this proof" functions as a prepositional phrase, modifying a clause or sentence by indicating the foundation or reason for a claim or conclusion. Ludwig AI confirms its usage in academic and scientific writing, where logical connections are critical.

Expression frequency: Rare

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Wiki

0%

Ludwig's WRAP-UP

In summary, the phrase "based on this proof" is a grammatically sound prepositional phrase used to indicate that a claim or conclusion is supported by a specific proof. As confirmed by Ludwig AI, it is primarily found in formal contexts, particularly in scientific and academic writing. While related phrases exist that convey similar meanings, "based on this proof" clearly signals a logical derivation from concrete evidence, adding credibility to an argument. When using this phrase, ensure the proof is readily available for reference and that claims remain within the bounds of what the proof directly supports.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

grounded in this proof

Replaces "based" with "grounded", suggesting a more foundational or fundamental connection to the proof.

derived from this proof

Emphasizes that something originates or stems from the proof.

according to this proof

Highlights that the information aligns with what the proof demonstrates.

as demonstrated by this proof

Shifts the focus to the proof itself as the source of evidence.

stemming from this proof

Suggests that something arises or originates directly from the proof.

relying on this proof

Focuses on the act of depending on the proof as a basis.

justified by this proof

Highlights that the proof provides a rationale or justification for something.

predicated on this proof

Indicates that something is founded or established on the basis of the proof.

informed by this proof

Implies that the proof has provided insight or understanding that influences something.

founded upon this proof

Similar to "grounded in", suggesting a strong and stable base derived from the proof.

FAQs

How can I use "based on this proof" in a sentence?

Use "based on this proof" to indicate that a statement, conclusion, or action is supported or justified by the evidence presented in a particular proof. For example, "Based on this proof, we can conclude that the theorem holds true".

What's a more formal way to say "based on this proof"?

Consider using alternatives such as "grounded in this proof" or "derived from this proof" for a more formal tone. These options emphasize a stronger connection to the evidence.

Is it correct to say "based off this proof"?

While "based off" is sometimes used colloquially, "based on" is generally considered more grammatically correct and appropriate in formal writing. Therefore, "based on this proof" is preferable.

What's the difference between "based on this proof" and "supported by this proof"?

"Based on this proof" implies a direct logical derivation or conclusion from the proof, while "supported by this proof" suggests that the proof provides evidence that strengthens or validates a claim, but may not be the sole basis for it.