let A be non empty set ; :: thesis: for f being Element of Funcs (A,COMPLEX) holds (ComplexFuncAdd A) . ((ComplexFuncZero A),f) = f
let f be Element of Funcs (A,COMPLEX); :: thesis: (ComplexFuncAdd A) . ((ComplexFuncZero A),f) = f

now :: thesis: for x being Element of A holds ((ComplexFuncAdd A) . ((ComplexFuncZero A),f)) . x = f . x

let x be Element of A; :: thesis: ((ComplexFuncAdd A) . ((ComplexFuncZero A),f)) . x = f . x
thus ((ComplexFuncAdd A) . ((ComplexFuncZero A),f)) . x = ((ComplexFuncZero A) . x) + (f . x) by Th1
.= 0c + (f . x) by FUNCOP_1:7
.= f . x ; :: thesis: verum

end;

hence (ComplexFuncAdd A) . ((ComplexFuncZero A),f) = f by FUNCT_2:63; :: thesis: verum