reserve x for set;
reserve a, b, c for Real;
reserve m, n, m1, m2 for Nat;
reserve k, l for Integer;
reserve p, q for Rational;
reserve s1, s2 for Real_Sequence;

theorem
  a>=0 implies 2-Root a = sqrt a
proof
  assume that
A1: a>=0 and
A2: 2-Root a <> sqrt a;
A3: sqrt a >= 0 by A1,SQUARE_1:def 2;
  sqrt a |^ 2 = (sqrt a)^2 by NEWTON:81
    .= a by A1,SQUARE_1:def 2;
  hence contradiction by A2,A3,Th19;
end;
