reserve i,j,n,k for Nat,
  a for Element of COMPLEX,
  R1,R2 for Element of i-tuples_on COMPLEX;

theorem Th15:
  a*mlt(R1,R2) = mlt(a*R1,R2)
proof
  thus a*mlt(R1,R2) = (multcomplex[;](a,id COMPLEX))*(mlt(R1,R2)) by Lm1
    .= multcomplex.:((multcomplex[;](a,id COMPLEX))*R1,R2) by FINSEQOP:26
    .= mlt(a*R1,R2) by Lm1;
end;
