is proved for

USAGE SUMMARY

The phrase "is proved for" is not commonly used in written English and may sound awkward.
It can be used in contexts where you are indicating that something has been demonstrated or established for a particular case or situation. Example: "The theorem is proved for all integers greater than zero."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

60 human-written examples

Our next theorem is proved for six self-mappings in Menger space, which extends earlier proved Theorem 3.1.

Journal of Inequalities and Applications

Uniqueness is proved for a regular solution.

Computers & Mathematics with Applications

Next, under proper assumptions, asymptotic stability is proved for constant commands, while bounded stability is proved for varying commands.

ISA Transactions

A criterion of goodness is proved for such measures.

Journal of Functional Analysis

A local uniqueness is proved for the inverse problem.

Journal of Computational Physics

The same result is proved for elliptic manifolds.

Journal of Functional Analysis

Almost sure convergence to a Nash equilibrium is proved for diminishing step sizes.

Automatica

A geometric rate of convergence in probability is proved for these iterative estimates to MLE.

Journal of Statistical Planning and Inference

The convergence of the algorithm is proved for communication networks with bounded delays.

IFAC Proceedings Volumes

The existence and uniqueness result is proved for a steady state of the Hamiltonian system.

IFAC Proceedings Volumes

The generalized Itô formula is proved for F(B t)) with F ∈ H* Rk).

Journal of Functional Analysis

Expert writing Tips

Best practice

When using "is proved for", ensure that the context clearly specifies the conditions or limitations under which the statement holds true. Be precise about the scope and boundaries of the proof.

Common error

Avoid claiming that something "is proved for" all cases when the proof only applies to a specific subset or scenario. Always specify the constraints and assumptions under which the proof is valid to prevent misinterpretations.

Linguistic Context

The phrase "is proved for" functions as a passive construction, indicating that a theorem, claim, or result has been rigorously demonstrated or verified under specific conditions. Ludwig's examples show its use in academic and scientific contexts to highlight the validation of a statement.

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 "is proved for" is a grammatically sound and common expression, especially within scientific and academic writing. As Ludwig AI indicates, it signifies that a statement or theorem has been rigorously demonstrated under specific conditions. While it is mostly confined to the scientific field, it’s crucial to specify the applicable constraints to avoid overgeneralization. Alternatives like "is demonstrated for" or "is established for" can be used to vary your writing, while still maintaining a high degree of formality. Ensure that you only assert something "is proved for" when you can back it up with solid evidence and reasoning.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

is demonstrated for

Replaces "proved" with "demonstrated", emphasizing the act of showing or illustrating the validity.

is established for

Substitutes "proved" with "established", highlighting the confirmation and acceptance of something as true.

is verified for

Uses "verified" instead of "proved", focusing on the confirmation of accuracy or correctness.

is validated for

Replaces "proved" with "validated", emphasizing the confirmation of the truth or accuracy of something.

has been shown for

Changes the structure to active voice with "has been shown", indicating that evidence supports something.

is confirmed for

Substitutes "proved" with "confirmed", highlighting that something has been supported or validated.

is ascertained for

Replaces "proved" with "ascertained", emphasizing the discovery or establishment of something definitely.

holds true for

Changes the structure to emphasize the validity of something under specific conditions.

is substantiated for

Uses "substantiated" instead of "proved", focusing on the provision of evidence to support the claim.

is borne out for

Emphasizes that something is supported by evidence or facts.

FAQs

How can I use "is proved for" in a sentence?

Use "is proved for" to indicate that a theorem, claim, or result has been successfully demonstrated or verified under specific conditions. For example, "The theorem "is proved for" all positive integers".

What are some alternatives to "is proved for"?

Alternatives include "is demonstrated for", "is established for", or "is verified for" depending on the specific nuance you want to convey.

In what contexts is "is proved for" commonly used?

"Is proved for" is most commonly used in mathematical and scientific contexts to indicate that a statement or theorem has been rigorously demonstrated to be true under certain conditions.

Is there a difference between "is proved for" and "is true for"?

"Is proved for" implies that a formal proof exists to support the statement, whereas "is true for" simply asserts the validity of the statement without necessarily implying a formal proof. Use "is proved for" when you want to emphasize the existence of a rigorous demonstration.