 reserve n,s for Nat;

theorem Th70:
  for x being number holds
    x in TriangularNumbers iff x is triangular
  proof
    let x be number;
    thus x in TriangularNumbers implies x is triangular;
    assume x is triangular; then
    consider n being Nat such that
A1: x = Triangle n;
    x = Polygon (3,n) by A1,Th40;
    hence thesis;
  end;
