IDA: Proof

Proof

|G| = |Gb₁| · |G_b₁|

= |Gb₁| · |G_b₁b₂| · |G_b₁,b₂|

= ...

= |Gb₁|··· |G_{b₁, ... ,
b_t-1}b_t| · |G_{b₁,
... , b_t}|

= |Gb₁|··· |G_{b₁, ... ,
b_t-1}b_t|.

\|G\|	=	\|Gb₁\| · \|G_b₁\|
	=	\|Gb₁\| · \|G_b₁b₂\| · \|G_b₁,b₂\|
	=	...
	=	\|Gb₁\|··· \|G_{b₁, ... , b_t-1}b_t\| · \|G_{b₁, ... , b_t}\|
	=	\|Gb₁\|··· \|G_{b₁, ... , b_t-1}b_t\|.