reserve u,v,x,x1,x2,y,y1,y2,z,p,a for object,
        A,B,X,X1,X2,X3,X4,Y,Y1,Y2,Z,N,M for set;
reserve e for object, X,X1,X2,Y1,Y2 for set;

theorem Th134:
  X c= Y \/ {x} implies x in X or X c= Y
proof
  assume that
A1: X c= Y \/ {x} and
A2: not x in X;
  X = X /\ (Y \/ {x}) by A1,XBOOLE_1:28
    .= X /\ Y \/ X /\ {x} by XBOOLE_1:23
    .= X /\ Y \/ {} by A2,Lm6,XBOOLE_0:def 7
    .= X /\ Y;
  hence thesis by XBOOLE_1:17;
end;
