For a monochrome layer $x$ of opacity $0\le o_x\le1 $ placed on another monochrome layer of opacity 1, the result given by the standard formula is $$\small\Pi\left({\bf C}_\varphi\right)=1+\sum_{n=1}^2\left(2-n-(-1)^no_{\chi(\varphi+1)}\right)\left(\chi(n+\varphi-1)-o_{\chi(n+\varphi-1)}\right),$$ the formula being of course explained in detail in this paper. We will eventually deduce a very simple theorem, generalize it and then see its validity with alternative formulas to this standard containing the same main properties here exposed.

翻译：对于透明度为$0\le o_x\le1$的单色图层$x$放置在透明度为1的另一单色图层上时，标准公式给出的结果是$$\small\Pi\left({\bf C}_\varphi\right)=1+\sum_{n=1}^2\left(2-n-(-1)^no_{\chi(\varphi+1)}\right)\left(\chi(n+\varphi-1)-o_{\chi(n+\varphi-1)}\right),$$ 该公式自然将在本文中详细阐述。我们最终将推导出一个非常简洁的定理，对其进行推广，并验证该定理与包含相同主要性质的其他替代公式在标准公式上的有效性。