reconsider e = FuncUnit X as Element of (Ring_of_BoundedLinearOperators X) ;
take e ; :: according to GROUP_1:def 1 :: thesis: for b₁ being Element of the carrier of (Ring_of_BoundedLinearOperators X) holds
( b₁ * e = b₁ & e * b₁ = b₁ )
thus for b₁ being Element of the carrier of (Ring_of_BoundedLinearOperators X) holds
( b₁ * e = b₁ & e * b₁ = b₁ ) by Lm1; :: thesis: verum