
theorem Th15:
  for A being non-empty partial UAStr, R being Relation of the carrier of A
  holds R|^(A,0) = R & R|^(A,1) = R|^A
proof
  let A be non-empty partial UAStr;
  let R be Relation of the carrier of A;
  consider F being ManySortedSet of NAT such that R|^(A,0) = F.0 and
A1: F.0 = R and
A2: 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.(0+1) = R|^A by A1,A2;
  hence thesis by A1,A2,Def6;
end;
