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 Th31:
  Sum(F^<*c*>) = Sum F + c
proof
  reconsider s=c as Element of COMPLEX by XCMPLX_0:def 2;
  reconsider F1=F as FinSequence of COMPLEX by Lm2;
  thus Sum(F^<*c*>) = Sum(F1^<*s*>)
    .= addcomplex.(addcomplex $$ F1,s) by FINSOP_1:4
    .= Sum F1 + c by BINOP_2:def 3
    .= Sum F + c;
end;
