reserve G for strict Group,
  a,b,x,y,z for Element of G,
  H,K for strict Subgroup of G,
  p for Element of NAT,
  A for Subset of G;

theorem
  for G being Group, H being Subgroup of G, h being Element of G st
  h in H holds H * h c= the carrier of H
proof
  let G be Group, H be Subgroup of G;
  let h be Element of G such that
A1: h in H;
    let a be object;
    assume a in H * h;
    then consider g being Element of G such that
A2: a = g * h and
A3: g in H by GROUP_2:104;
    g * h in H by A1,A3,GROUP_2:50;
    hence thesis by A2;
end;
