Let $H$ be any graph and $T_1$ and $T_2$ be spanning trees for $H$. Prove that the size of $T_1$ equals the size of $T_2$.
Proof: $T_1$ has an edge set $\{\{v_1,v_2\},\{v_2,v_3\},\dots,\{v_{n-1},v_n\}\}$ which has $n-1$ elements.
$T_2$ has an isomorphic labelling, $\{\{v_1,v_2\},\{v_2,v_3\},.\dots,\{v_{m-1},v_{m}\}\}$ which has $m-1$ elements where $m$ and $n$ are the final vertices, and hence $m=n$.
Thus both trees are of the same size.
Critique? Is this even a valid proof?