Strict monotonicity of the grid enumeration $x_L = (L \bmod m_1) + M\lfloor L/m_1 \rfloor$ for $M \ge m_1$

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Strict monotonicity of the grid enumeration $x_L = (L \bmod m_1) + M\lfloor L/m_1 \rfloor$ for $M \ge m_1$ · Prove2Me