Incremental View Maintenance for projection
Just realize the reason after posting the question.
Counterexample:
R =

A  B

1  2

1  1

1  1

ΔR =

A  B

1  1

1  1

1  1

Assume we want ΠA(R - ΔR)

The true answer is first R - ΔR:

A  B

1  2

Then project A:

A

1

However, if ΠA(R - ΔR) = ΠA(R) - ΠA(ΔR).
ΠA(R):

A

1 

1 

1 

ΠA(ΔR):

A

1 

1 

1

ΠA(R) - ΠA(ΔR) = ∅

ΠA(R - ΔR) = ΠA(R) - ΠA(R min ΔR).

R min ΔR:

A  B

1  1

1  1

ΠA(R min ΔR):

A

1

1

ΠA(R) - ΠA(R min ΔR):

A

1