let c1, c2 be Complex; :: thesis: ( c2 <> 0 & (Arg c2) - (Arg c1) >= 0 implies angle (c1,c2) = (Arg c2) - (Arg c1) )
assume that
A1: c2 <> 0 and
A2: (Arg c2) - (Arg c1) >= 0 ; :: thesis: angle (c1,c2) = (Arg c2) - (Arg c1)
thus angle (c1,c2) = Arg (Rotate (c2,(- (Arg c1)))) by A1, COMPLEX2:def 3
.= (Arg c2) - (Arg c1) by A1, A2, Lm10 ; :: thesis: verum