theorem Th47:
  for R being real-membered set for f being Function of T,R, t being Point of T
  st x in Seg n holds incl(f,n).t.x = f.t
  proof
    let R be real-membered set;
    let f be Function of T,R;
    let t be Point of T;
    assume
A1: x in Seg n;
    thus incl(f,n).t.x = (n |-> f.t).x by Def4
    .= f.t by A1,FINSEQ_2:57;
  end;
