How can this possibly fail to partition True(x) from Untrue(x) for every formal system?

[PeteOlcott]

When we specify that True(x) is the consequences of the subset of the
of conventional formal proofs of mathematical logic having true premises
then True(x) is always defined and never undefinable.

[Eodnhoj7]

When we specify that True(x) is the consequences of the subset of the
of conventional formal proofs of mathematical logic having true premises
then True(x) is always defined and never undefinable.

False, as the mathematical function of subset is never fully defined except through continuous proofs.

All functions of mathematics are grounded in an necessary continuity of definition, just like the number line.

The mathematical function must continuously exist through a continuum of numbers and as such is as undefined as infinity.

However the function must be true, for the truth statement to exist.