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 Th36:
  Sum(i |-> c) = i*c
proof
  reconsider c as Element of COMPLEX by XCMPLX_0:def 2;
  defpred P[Nat] means Sum($1 |->c) = $1*c;
A1: for i st P[i] holds P[(i+1)]
  proof
    let i such that
A2: Sum(i |-> c) = i*c;
    thus Sum((i+1) |-> c) = Sum((i |-> c)^<*c*>) by FINSEQ_2:60
      .= i*c + 1*c by A2,Th31
      .= (i+1)*c;
  end;
A3: P[0];
  for i holds P[i] from NAT_1:sch 2(A3,A1);
  hence thesis;
end;
