reconsider e = One_ ((BoundedFunctions X),(RAlgebra X)) as Element of (R_Normed_Algebra_of_BoundedFunctions X) ;
take e ; :: according to GROUP_1:def 1 :: thesis: for b₁ being Element of the carrier of (R_Normed_Algebra_of_BoundedFunctions X) holds
( b₁ * e = b₁ & e * b₁ = b₁ )
thus for b₁ being Element of the carrier of (R_Normed_Algebra_of_BoundedFunctions X) holds
( b₁ * e = b₁ & e * b₁ = b₁ ) by Lm3; :: thesis: verum