
theorem RAt:
for R being Ring,
    S being RingExtension of R
for T being Subset of S holds T is Subset of RAdj(R,T)
proof
let R be Ring, S be RingExtension of R; let T be Subset of S;
set P = RAdj(R,T);
now let o be object;
  assume A: o in T;
  then reconsider a = o as Element of S;
  for U be Subring of S st R is Subring of U & T is Subset of U
    holds o in U by A;
  then a in carrierRA(T);
  hence o in the carrier of P by dRA;
  end;
hence thesis by TARSKI:def 3;
end;
