let X be Complex_Banach_Algebra; :: thesis: X is well-unital
let x be Element of X; :: according to VECTSP_1:def 6 :: thesis: ( x * (1. X) = x & (1. X) * x = x )
thus ( x * (1. X) = x & (1. X) * x = x ) by VECTSP_1:def 4, VECTSP_1:def 8; :: thesis: verum