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We prove consistency results of our method.
We prove consistency at all points, including the sonic points.
We prove consistency and stability of the proposed dG scheme.
Moreover, under mild assumptions, I prove consistency of this smooth approximation for both minimizers and stationary points of the target optimization problem.
We prove consistency and convergence to mixtures of normal laws, where the mixing variates depend on the chronological local time of the underlying process, that is the time spent by the process in the vicinity of a spatial point.
In order to prove consistency of the proposed values the vaporization enthalpies obtained by combination of both were compared to vaporization enthalpies obtained by the group-additivity method and the correlation-gas chromatography method.
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It is this latter feature that makes the calculus convenient for the purpose of proving consistency.
We prove test consistency and propose a bootstrap procedure to obtain p-values.
The next obvious task in proof theory, after the proof of the consistency of arithmetic, was to prove the consistency of analysis, i.e., of the theory of real numbers.
For example, Rosser's provability predicate mentioned above would not do; one can prove the "consistency" of F in F, if consistency is expressed in terms of Rosser's provability predicate.
One can prove these consistency results along the lines of the consistency proof for λ by extending the Church-Rosser theorem to the wider senses of derivability of these theories.
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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