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State/Every lax basis is contained in exactly two lax superbases

Definition of Every lax basis is contained in exactly two lax superbases: Suppose that $\{ \pm \vec e, \pm \vec f \}$ is a lax basis. Then, there exist precisely two lax superbases containing $\{ \pm \vec e, \pm \vec f \}$. Equivalently, there exist precisely two primitive lax vectors $\pm \vec g,\pm \vec h$ such that: $$\{ \pm \vec e,\pm \vec f,\pm \vec g \} \mbox{ and } \{\pm \vec e,\pm \vec f,\pm \vec h \} \mbox{ are lax superbases}.$$

Logical Connections

This definition logically relies on the following definitions and statements: Def/Lax basis, Def/Lax superbasis, Def/Lax vector

The following statements and definitions logically rely on the material of this page: Def/Domain topograph

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