Function compile_theory_for_ui 

pub fn compile_theory_for_ui(input: &str) -> TheoryCompileResult

Compile a program’s formal development end to end: collect every ## Axiom (a shared premise base) and every ## Theory block’s Axiom/Theorem declarations, then prove the theorems in citation order, each kernel-certified by the multi-theorem driver. This is the seam that turns a Tarski-style source file into a verified development.