
theorem Th22:
  for F being finite set, A being FinSequence of bool F, B being Reduction of A
  for C being Reduction of B holds C is Reduction of A
proof
  let F be finite set, A be FinSequence of bool F, B be Reduction of A;
  let C be Reduction of B;
A1: for i being Element of NAT st i in dom A holds C.i c= A.i
  proof
    let i be Element of NAT;
    assume
A2: i in dom A;
    then i in dom B by Def6;
    then
A3: C.i c= B.i by Def6;
    B.i c= A.i by A2,Def6;
    hence thesis by A3;
  end;
  dom B = dom C by Def6;
  hence thesis by A1,Def6;
end;
