reserve s for set,
  i,j for natural Number,
  k for Nat,
  x,x1,x2,x3 for Real,
  r,r1,r2,r3,r4 for Real,
  F,F1,F2,F3 for real-valued FinSequence,
  R,R1,R2 for Element of i-tuples_on REAL;

theorem Th96:
  for F being complex-valued FinSequence, r being Complex holds
    Product (F^<*r*>) = Product F * r
proof
  let F be complex-valued FinSequence, r be Complex;
  reconsider p = r as Element of COMPLEX by XCMPLX_0:def 2;
  rng F c= COMPLEX & rng (F^<*p*>) c= COMPLEX by VALUED_0:def 1;
  then reconsider Fr = F^<*r*>, Ff = F as FinSequence of COMPLEX
  by FINSEQ_1:def 4;
  thus Product (F^<*r*>) = multcomplex $$ Fr by Def13
    .= multcomplex.(Product Ff,p) by FINSOP_1:4
    .= Product F * r by BINOP_2:def 5;
end;
