proof line

USAGE SUMMARY

The phrase "proof line" is correct and usable in written English.
It can be used in contexts related to editing, publishing, or any situation where a line of text is being verified for accuracy or correctness. Example: "Before we finalize the document, please ensure that the proof line is accurate and free of errors."

✓ Grammatically correct

Science

News & Media

Human-verified examples from authoritative sources

Exact Expressions

9 human-written examples

The proof line is similar to that of Theorem 4.1.

Advances in Difference Equations

We follow the proof line as in [16].

Journal of Inequalities and Applications

The proof line now follows from the proofs of Theorem 2.3 and [15, Theorem ].

Fixed Point Theory and Applications

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

Advances in Difference Equations

Along a similar proof line, we can obtain the following result for the Ishikawa-type iteration process.

Fixed Point Theory and Applications

Following the proof line in Case 1, we can verify lim k → ∞ 〈 ∇ f ( u ) − ∇ f ( p ), x m k + 1 − p 〉 ≤ 0 (3.18).

Journal of Inequalities and Applications

Human-verified similar examples from authoritative sources

Similar Expressions

50 human-written examples

Moreover, the proof lines of Theorem 4.2 in [6] are really long.

Fixed Point Theory and Applications

But the authors found some mistakes in the proof lines of their main result.

Journal of Inequalities and Applications

Following the proof lines of Theorem 3.1, we can show the following.

Fixed Point Theory and Applications

Again, from the proof lines of Theorem 3.1, we have the following conclusions: (3.19).

Fixed Point Theory and Applications

Also, the proof lines of Theorem 2.4 that are not correct are the following ones (see p.1902, lines 22-32): where q > 0 such that m < n q.

Journal of Inequalities and Applications

Expert writing Tips

Best practice

When referring to a specific methodology, cite the original source or theorem from which the "proof line" is derived.

Common error

Avoid claiming originality for a "proof line" if it's a standard technique. Always verify and credit the original source to maintain academic integrity.

Linguistic Context

The phrase "proof line" functions as a noun phrase that denotes a specific method, step, or sequence within a mathematical or logical demonstration. Ludwig AI indicates its use is primarily within scientific and academic contexts.

Expression frequency: Uncommon

Frequent in

Science

80%

News & Media

10%

Formal & Business

5%

Less common in

Encyclopedias

2%

Wiki

2%

Reference

1%

Ludwig's WRAP-UP

In summary, "proof line" is a noun phrase predominantly used in scientific and academic writing to denote a specific step or method within a proof. As Ludwig AI confirms, it serves to link a current demonstration to prior established techniques. Although grammatically correct, its formality makes it less common in general writing, with primary usage in the science domain. When using this phrase, it's best practice to cite the original source to maintain academic integrity. Alternatives like "evidence line" or "line of reasoning" may be suitable depending on the context. Overall, use "proof line" in formal, technical contexts where a precise reference to a proof methodology is required.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

evidence line

Focuses on the 'evidence' aspect of a line of reasoning rather than the formal 'proof'.

line of reasoning

Emphasizes the sequential steps in building an argument.

argument's trajectory

Describes the general direction and flow of an argument.

proof internet

Specifically refers to proofs found or discussed online.

demonstration line

Highlights the 'demonstration' aspect of a mathematical or logical proof.

proof thread

Implies a continuous and interconnected chain of reasoning.

logical progression

Stresses the logical order and sequence of steps.

sequence of deductions

Emphasizes the deductive nature of the proof.

chains of evidence

Implies multiple pieces of evidence connected to support a claim.

inferential pathway

Highlights the path of inference from premises to conclusion.

FAQs

How can I use "proof line" in a sentence?

You can use "proof line" to refer to a specific method or step in a mathematical or logical demonstration. For example, 'The "proof line" now follows from the proofs of Theorem 2.3' or 'Following the "proof line" in Case 1, we can verify...'.

What are some alternatives to "proof line"?

Alternatives include "evidence line", "line of reasoning", or "argument's trajectory". The best choice depends on the specific context and the aspect you want to emphasize.

What does it mean to 'follow the proof line'?

To 'follow the proof line' means to replicate or adapt a particular method or set of steps used in a previous proof. It suggests using a similar approach to solve a related problem.

In what contexts is "proof line" typically used?

"Proof line" is frequently used in mathematical and scientific literature to describe a particular step or technique used in a demonstration or derivation. It is also used when referencing or adapting a method from another source.