R : Type u_2
inst✝⁵ : CommSemiring R
M : Submonoid R
S : Type ?u.2882462
inst✝⁴ : CommSemiring S
inst✝³ : Algebra R S
P : Type ?u.2882629
inst✝² : CommSemiring P
A : Type u_1
inst✝¹ : CommSemiring A
inst✝ : Algebra A R
m : A
⊢ ↑(algebraMap ((fun x => R) m) (Localization M)) (↑(algebraMap A R) m) = ↑(algebraMap A (Localization M)) m
R : Type u_2
inst✝⁵ : CommSemiring R
M : Submonoid R
S : Type ?u.2882462
inst✝⁴ : CommSemiring S
inst✝³ : Algebra R S
P : Type ?u.2882629
inst✝² : CommSemiring P
A : Type u_1
inst✝¹ : CommSemiring A
inst✝ : Algebra A R
m : A
⊢ mk (↑(algebraMap A R) m) 1 = ↑(algebraMap A (Localization M)) m
rw [mk_eq_mk', mk'_eq_iff_eq_mul, Submonoid.coe_one, map_one, mul_one]
no goals
R : Type u_2
inst✝⁵ : CommSemiring R
M : Submonoid R
S : Type ?u.2882462
inst✝⁴ : CommSemiring S
inst✝³ : Algebra R S
P : Type ?u.2882629
inst✝² : CommSemiring P
A : Type u_1
inst✝¹ : CommSemiring A
inst✝ : Algebra A R
m : A
⊢ ↑(algebraMap ((fun x => R) m) (Localization M)) (↑(algebraMap A R) m) = ↑(algebraMap A (Localization M)) m
rfl