Assumption of proof with contrapositive I want to prove by proof with contrapositive that
$\left \| u(0) \right \|=0 $ then $\left \| u(t) \right \|=0$ for all t belongs to $\left [ 0,T \right ]$.
Then I write
$\left \| u(t) \right \|\neq 0$ then $\left \| u(0) \right \|\neq 0$ for all t belongs to $\left [ 0,T \right ]$.
Is it correct ?

The contrapositive of
If $∥u(0))∥=0$, then $‖u(t))‖=0$ for all $t$ belonging to $[0,T]$.
is the following:
If $‖u(t))‖\ne 0$ for some $t$ belonging to $[0,T]$, then $∥u(0))∥\ne 0$.
