Pi.constRingHom_eq_algebraMap

theorem Pi.constRingHom_eq_algebraMap : ∀ (R : Type u_1) (A : Type u_2) [inst : CommSemiring R], Pi.constRingHom A R = algebraMap R (A → R)

This theorem states that for any types `R` and `A`, if `R` is a commutative semiring, then the ring homomorphism that constantly maps any value from `A` to a fixed value in `R` (denoted by `Pi.constRingHom A R`) is equivalent to the ring homomorphism induced by the algebra structure of `R` over `A` (denoted by `algebraMap R (A → R)`). In other words, both mappings are identical. This links the concepts of constant functions and algebraic embeddings in the context of ring theory.

More concisely: For any commutative semiring `R` and type `A`, the constant ring homomorphism `Pi.constRingHom A R` from `A` to `R` is equal to the algebra map `algebraMap R (A → R)` from `A` to `R`.