All but last projection can be ignored:

• π_L1 ( π_L2 ( ... π_Ln (R)))   →   π_L1 (R)

Projections can be pushed into joins:

• π_L (R  ⋈_c S)   ↔   π_L ( π_M(R)  ⋈_c  π_N(S) )

• M and N must contain all attributes needed for c
• M and N must contain all attributes used in L   (L ⊂ M∪N)