Edited sentence: For any two projection, if E ∩ F = V, then the unique projection J with image V and kernel the orthogonal complement of V is the meet of E and F.If E and F are projections, then E ≤ F iff imE ⊆ imF.In the case of Mn(C) more can be said.Since projections form a meet-semilattice, the partial isometries on Mn(C) from an inverse semigroup with the product