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"rigorous proof" is a correct and usable phrase in written English.
You can use this phrase when referring to evidence that is presented in an in-depth and thorough manner. For example, "The lawyer provided rigorous proof to back his client's case."
Exact(58)
A rigorous proof is still lacking.
Gauss also gave the first rigorous proof of the law.
Unfortunately, there is no rigorous proof of convergence to date.
Universities permit radical ideas because they demand rigorous proof before accepting ideas as facts.
Dr. Arnold provided a rigorous proof in 1963 for one set of circumstances.
Chapter 2 discusses the rigorous proof of chaos in the Four-Element Chua's circuit.
For a more rigorous proof, see The Chain Rule - a More Formal Approach.
In this paper, we will give a rigorous proof of some arguments of Ishimura.
Unfortunately, there is no a rigorous proof of convergence to date.
The inequality is of mathematical interest in its own right, and is given a rigorous proof.
Rigorous proof shows that the attitude can be stabilized to the equilibrium in finite time.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com