The method by which mathematics arrives at its equations is the method of substitution.

For equations express the substitutability of two expressions, and we proceed from a number of equations to new equations,
replacing expressions by others in accordance with the equations.

6.241 Thus the proof of the proposition 2 × 2 = 4 runs:

(^{v})^{µ}'x=^{v×µ}'x
Def.

^{2×2}'x = (^{2})^{2}'x = (^{2})^{1+1}'x = ^{2}'^{2}'x = ^{1+1}'^{1+1}'x

= (')'(')'x = ''''x = ^{1+1+1+1}'x = ^{4}'x.