
theorem Th16:
  for A being non-empty partial UAStr, i being Nat,
  R being Relation of the carrier of A holds R|^(A,i+1) = R|^(A,i)|^A
proof
  let A be non-empty partial UAStr;
  let i be Nat;
  let R be Relation of the carrier of A;
  consider F being ManySortedSet of NAT such that
A1: R|^(A,i) = F.i and
A2: F.0 = R and
A3: for i being Nat, R being Relation of the carrier of A st
  R = F.i holds F.(i+1) = R|^A
  by Def6;
  F.(i+1) = R|^(A,i)|^A by A1,A3;
  hence thesis by A2,A3,Def6;
end;
