Say, I have finite tuple $x$:
$ x \in X \times X' \times X'' \times \ldots $
Now I define a $Y$, a set of predicate functions over this tuple:
$\forall y \in Y. y: X \times X' \times X'' \times \ldots \to \mathbb{B}$
But I want to have a special property on this set $Y$.
$$\forall x. \forall y, y' \in Y. y \not = y' \Rightarrow y(x) \not = y'(x) = 1$$ $$\forall x. \exists y \in Y. y(x) = 1$$
Basically no matter the configuration of $x$, there should never be two, but at least one function in Y, which both map it to True. I.e. the mapping $X \times X' \times X'' \times \ldots \to Y$ is a function. When this function is also surjective, the set Y becomes a minimal solution fulfilling the above properties.
For example, I have a tuple $x \in X \times X \times X$, where $X = \{a,b\}$
And I have a set of functions $Y = \{y_1, y_2, y_3, y_4\}$
$$ y_1, y_2, y_3, y_{4}: X \times X \times X \to \mathbb{B} \\ y_1: (a, a, a) \mapsto 1 \\ y_1: (a, a, b) \mapsto 1 \\ y_1: (a, b, a) \mapsto 1 \\ y_1: (\_, \_, \_) \mapsto 0 \\ y_2: (a, b, b) \mapsto 1 \\ y_2: (\_, \_, \_) \mapsto 0 \\ y_3: (b, a, a) \mapsto 1 \\ y_3: (\_, \_, \_) \mapsto 0 \\ y_4: (b, a, b) \mapsto 1 \\ y_4: (b, b, a) \mapsto 1 \\ y_4: (b, b, b) \mapsto 1 \\ y_4: (\_, \_, \_) \mapsto 0 \\ $$
Now to my question. Usually when I discover any kind of helpful notion, I expect that I only rediscover it, and it probably already has a name.