I'm trying to write a formal proof that there exists a bijection between two sets,
Namely, If I take $E$ a set of integers and $(x_i)_{i\in\{1,\dots,n\}}$ a sequence of elements of $E$ sorted in strictly (that is no duplicates) increasing order, then the mapping defined by :
$$\{x_1,\dots,x_n\}\mapsto (x_1,\dots,x_n)$$ where the result is the ordered $n$-tuple, should be a bijection.
I wrote down what sorted in increasing order means :
$$\forall i \in \{1,\dots,n-1\},\quad x_i<x_{i+1}$$
It follows clearly that $E$ must contain (shifting if necessary) $\{1,\dots,n\}$ for this to work, so we can assume $E=\{1,\dots,m\}$ with $m\geq n$
But I don't know how to go on with the proof.
Any help will be appreciated
thanks!