6.241 Thus the proof of the proposition 2 × 2 = 4 runs:
( Ω ν ) μ ′ x = Ω ν × μ ′ x Def. {\displaystyle (\Omega ^{\nu })^{\mu \prime }x=\Omega ^{\nu \times \mu \prime }x{\text{ Def.}}}
Ω 2 × 2 ′ x = ( Ω 2 ) 2 ′ x = ( Ω 2 ) 1 + 1 ′ x = Ω 2 ′ Ω 2 ′ x = Ω 1 + 1 ′ Ω 1 + 1 ′ x {\displaystyle \Omega ^{2\times 2\prime }x=(\Omega ^{2})^{2\prime }x=(\Omega ^{2})^{1+1\prime }x=\Omega ^{2\prime }\Omega ^{2\prime }x=\Omega ^{1+1\prime }\Omega ^{1+1\prime }x}
( Ω ′ Ω ) ′ ( Ω ′ Ω ) ′ x = Ω ′ Ω ′ Ω ′ Ω ′ x = Ω 1 + 1 + 1 + 1 ′ x = Ω 4 ′ x {\displaystyle (\Omega '\Omega )^{\prime }(\Omega '\Omega )^{\prime }x=\Omega '\Omega '\Omega '\Omega 'x=\Omega ^{1+1+1+1\prime }x=\Omega ^{4\prime }x}
