 reserve R for commutative Ring;
 reserve A,B for non degenerated commutative Ring;
 reserve h for Function of A,B;
 reserve I0,I,I1,I2 for Ideal of A;
 reserve J,J1,J2 for proper Ideal of A;
 reserve p for prime Ideal of A;
 reserve S,S1 for non empty Subset of A;
 reserve E,E1,E2 for Subset of A;
 reserve a,b,f for Element of A;
 reserve n for Nat;
 reserve x,o,o1 for object;
 reserve m for maximal Ideal of A;
 reserve p for prime Ideal of A;
 reserve k for non zero Nat;

theorem Th30:
  I c= sqrt I
  proof
    let x be object;
    assume
A1: x in I; then
    reconsider x as Element of A;
    x|^1 in I by A1,BINOM:8; then
    x in {a where a is Element of A: ex n being
      Element of NAT st a|^n in I};
    hence thesis by IDEAL_1:def 24;
  end;
