Contraction distributive property in GA

[mnb96]

Hello,
according to my book of 'Geometric Algebra' the operation of Left-Contraction for Blades has a distributive property in respect to addition. However the authors do not prove it, nor they give the smallest hint on how to derive it.

The property says that:

$$(\textbf{A+B})|\textbf{C}=\textbf{A}|\textbf{C}+\textbf{B}|\textbf{C}$$

where the symbol | denotes Left-Contraction.
Does anyone have a clue on how to prove that identity?

 

[mnb96]

Apparently the answer should be that the left contraction is constructed axiomatically by using the operations $$\wedge$$ (wedge product) and $$\ast$$ (scalar product), which are both bilinear. It follows, that the left-contraction must be bilinear too.