now :: thesis: for h being non-zero 0 -convergent Complex_Sequence holds
( (h ") (#) ((R1 - R2) /* h) is convergent & lim ((h ") (#) ((R1 - R2) /* h)) = 0c )

let h be non-zero 0 -convergent Complex_Sequence; :: thesis: ( (h ") (#) ((R1 - R2) /* h) is convergent & lim ((h ") (#) ((R1 - R2) /* h)) = 0c )
A4: (h ") (#) ((R1 - R2) /* h) = (h ") (#) ((R1 /* h) - (R2 /* h)) by CFCONT_1:14
.= ((h ") (#) (R1 /* h)) - ((h ") (#) (R2 /* h)) by COMSEQ_1:15 ;
A5: ( (h ") (#) (R1 /* h) is convergent & (h ") (#) (R2 /* h) is convergent ) by Def3;
hence (h ") (#) ((R1 - R2) /* h) is convergent by A4; :: thesis: lim ((h ") (#) ((R1 - R2) /* h)) = 0c
( lim ((h ") (#) (R1 /* h)) = 0c & lim ((h ") (#) (R2 /* h)) = 0c ) by Def3;
hence lim ((h ") (#) ((R1 - R2) /* h)) = 0c - 0c by A5, A4, COMSEQ_2:26
.= 0c ;
:: thesis: verum

end;

hence for b₁ being PartFunc of COMPLEX,COMPLEX st b₁ = R1 - R2 holds
( b₁ is total & b₁ is RestFunc-like ) ; :: thesis: verum