 reserve x,y,X,Y for set;
reserve G for non empty multMagma,
  D for set,
  a,b,c,r,l for Element of G;
reserve M for non empty multLoopStr;
reserve H for non empty SubStr of G,
  N for non empty MonoidalSubStr of G;

theorem Th34:
  G is idempotent implies H is idempotent
proof
  assume
A1: G is idempotent;
A2: carr(H) c= carr(G) by Th23;
  now
    let a be Element of H;
    reconsider a9 = a as Element of G by A2;
    thus a*a = a9*a9 by Th25
      .= a by A1,Th7;
  end;
  hence thesis by Th7;
end;
