# Ordered Tuple/Equality

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## Theorem

Let:

$(1): \quad \sequence {a_m} = \tuple {a_1, a_2, \ldots, a_m}$

and

$(2): \quad \sequence {b_n} = \tuple {b_1, b_2, \ldots, b_n}$

be ordered tuples for some $m, n \in \N_{>0}$.

Then:

$\sequence {a_m} = \sequence {b_n} \iff n = m \land \forall j \in \N^*_n: a_j = b_j$