>>21Every correct theorem is a tautology as demonstrated by its proof. That's because any mathematically correct proof is a demonstration of how the axioms (which you for some reason call " environment of semantics") automatically imply the theorem's statement.
E.g. the arithmetic axioms along with the definition of a prime number automatically imply the infinitude of the set of prime numbers; to state that the set of prime numbers is infinite would be a tautology yet mathematicians call it a theorem. Choosing a different definition of a prime number or different arithmetic axioms would create different tautologies (like non-Euclidean geometries lead to theorems different from Euclidean geometry theorems) but the mathematicall process is always the same: propose a statement then check whether it's a tautology or wrong. There are no other options in mathematics, which is why proof verification exists and people like Voevodsky are working to make all mathematics automatic and computer-verified. Mathematics is cancer of the human mind and it's time we freed everyone from the dolorous shackles of mindlessly trudging through tautologies.