Prove these two definitions of nondeterministic polynomial time are equivalent.

NTM definition

NP $=$NTIME$(poly(n))={?}_u{?}_{\text{k}\text{i}\text{n}\text{N}}$NTIME$(n^k)$

Verifier definition

$Lin$ NP iff $E$ deterministic TM $V,T(V)=$ poly $(n),$ st $xinL$ iff $E^{p}y$ st $V$ accepts $(x,y)$