The special theory of relativity shows that intervals are invariant under Lorentz transform in the Minkowski space -time.
But how can we prove (any postulates or theory) that the length is an invariant under Galilean transform in the Euclidean space?

The special theory of relativity shows that intervals are invariant under Lorentz transform in the Minkowski space -time.
But how can we prove (any postulates or theory) that the length is an invariant in the Euclidean space?

The special theory of relativity shows that intervals are invariant under Lorentz transform in the Minkowski space -time.
But how can we prove(any postulates or theory) that the length is an invariant under Galilean transform in the Euclidean space?

The special theory of relativity shows that intervals are invariant under Lorentz transform in the Minkowski space -time.
But how can we prove  (any postulates or theory) that the length is an invariant under Galilean transform in the Euclidean space?