Some properties of shift mappingσf·σg:lim(X,f·g)→lim(X,f?g) over double reverse limit space of continuous mapping f·X→X,g?X→X over non-empty compact metric space are studied,if f,g is surjection,then shift mapping σf·σgis weak rigidity(uniform rigidity)if and only if f?gis weak rigidity(uniform rigidity),f?g is almost equi-continuous,then σf·σg is also almost equi-continuous.