Theory
Exponential
The graph of exponential is definable by -fomrula, and its inductive properties are proved in .
instance LO.ISigma0.exponential_definable
[M ⊧ₘ* 𝐈𝚺₀] : 𝚺₀-Relation (Exponential : M → M → Prop)
lemma LO.ISigma0.Exponential.exponential_zero_one [M ⊧ₘ* 𝐈𝚺₀] :
Exponential 0 1
lemma LO.ISigma0.Exponential.exponential_succ_mul_two
[M ⊧ₘ* 𝐈𝚺₀] {x y : M} :
Exponential (x + 1) (2 * y) ↔ Exponential x y
Other basic functions, such as are defined by using exponential.