reserve s for set,
  i,j for Nat,
  c,c1,c2,c3 for Complex,
  F,F1,F2 for complex-valued FinSequence,
  R,R1,R2 for i-element complex-valued FinSequence;

theorem Th22:
  c1*(i|->c2) = i|->(c1*c2)
proof
  reconsider s1=c1, s2=c2 as  Element of COMPLEX by XCMPLX_0:def 2;
  s1*(i|->s2) = i|->((multcomplex[;](s1,id COMPLEX)).s2) by FINSEQOP:16
             .= i|->(c1*c2) by Lm1;
  hence thesis;
end;
