Tuples

Definition: $n$-Tuple

An $n$-Tuple $(a_1,\cdots ,a_n)$ is a set of $n$ ordered pairs

$$\{(1,a_1),\cdots ,(n,a_n)\}$$

Theorem: Equality of $n$-Tuples

Two $n$-tuples $(a_1,\cdots ,a_n)$ and $(b_1,\cdots ,b_n)$ are equal if and only if $a_1=b_1,\cdots ,a_n=b_n$:

$$(a_1,\cdots ,a_n)=(b_1,\cdots ,b_n)⟺a_1=b_1\wedge \cdots \wedge a_n=b_n$$

PROOF

TODO