The supplied source code for the module IndisputableMonolith.Foundation.ArithmeticFromLogic is truncated at the end of Section 5b (le_antisymm). Consequently, the specific theorem embed_add is not present in the provided text.
From the module's docstring, we know that the framework uses a subsequent "Section 5 ('Embedding into ℝ₊')" to establish a structural map from the inductive LogicNat type to the multiplicative group of positive reals via the iteration of a generator. Conceptually, an embed_add theorem in this context typically proves that addition in LogicNat homomorphically maps to multiplication of the generator's iterations in ℝ₊ ($ \gamma^{a+b} = \gamma^a \gamma^b $). This embedding is the crucial step that ties the abstract Peano structure (recovered in the visible sections) back to the concrete physical comparison operator.
Because the formal declaration is missing from the supplied slice, I cannot show its Lean statement, list its immediate Lean dependencies, or specify exactly what it does not prove. No theorems can be cited.