I know that:
Hypothesis 1 (Girsanov Theorem)
Let $\theta=\begin{Bmatrix} \theta_t \end{Bmatrix}_{t\in [0,T]}$ be a square-integrable and $\Im_t$-adapted process such that $\mathbb{E}[e^{\frac{1}{2}\int_0^T|\theta_s|^2ds}]<+\infty$ (Novikov condition). Let $M_t=e^{\begin{Bmatrix} \int_0^t\theta_sdW_s-\frac{1}{2}\int_0^t\theta_s^2ds \end{Bmatrix}},t\in [0,T]$ be the only solution of the SDE $\left\{\begin{matrix} dM_t=M_t\theta_tdW_t\\M_0=1 \end{matrix}\right.$.
So exists a probability measure $\mathbb{Q}\sim\mathbb{P}$ which admits equivalent martingale if the Radon-Nikodym derivative $L:=\frac{d\mathbb{Q}}{d\mathbb{P}}|_{\Im}$ is expressed in terms of exponential martingal:
$L=M_t\Rightarrow \mathbb{E}^{\mathbb{Q}}[X]=\mathbb{E}^{\mathbb{P}}[LX],\forall X=\begin{Bmatrix} X_t \end{Bmatrix}_{t\in [0,T]}$ generic process on $(\Omega, \Im, \begin{Bmatrix} \Im_t \end{Bmatrix}_{t\in [0,T]},\mathbb{P})$ and $W_t^{\mathbb{Q}}:=W_t^{\mathbb{P}}-\int_0^t\theta_sds$.
Hypothesis 2 (Arbitrage freedom)
Let $S^k=\begin{Bmatrix} S_t^k \end{Bmatrix}_{t\in [0,T]}$ an $\Im_t$-adapted process with Ito's dynamics. Let $V_t(\Theta):=\sum_{k=1}^n \theta_t^k S_t^k$ be a function of $\Theta:=(\theta_t^1,...,\theta_t^n),\forall t\in [0,T],\theta_t^k \in \mathbb{R}$ with dynamics $dV_t(\Theta)=\sum_{k=1}^n[\theta_t^kdS_t^k+d\theta_t^kS_t^k]$ for $d\theta_t^kS_t^k\equiv \theta_t^kD_t^kS_t^kdt.$
So if $\exists \mathbb{Q}\sim \mathbb{P}:S_t^k=\mathbb{E}^{\mathbb{Q}}[e^{-\int_t^Tr_sds}S_T^k|\Im_t]\Rightarrow V_t(\Theta) \operatorname{is a martingale}\Rightarrow \operatorname{no arbitrages}$.
Hypothesis 3 (Replicability)
For $u_S,u_B=(1-u_S)\in \mathbb{R}^+$, for $B_t$ solution of $\left\{\begin{matrix} dB_t=r_tB_tdt\\B_0=1 \end{matrix}\right.$ and for $d\Pi:=u_sdS_t+(1-u_S)dB_t,\Pi=\begin{Bmatrix} \Pi_t \end{Bmatrix}_{t\in [0,T]}$, we have $\frac{d\Pi}{\Pi}=\frac{dF_t}{F_t}$ with $\frac{dF_t}{F_t}=\frac{1}{F}[\frac{\partial F}{\partial t}+\mu S_t \frac{\partial F}{\partial S_t}+\frac{\sigma^2 S_t^2}{2}\frac{\partial^2 F}{\partial S_t^2}]dt+\frac{\sigma S_t}{F}\frac{\partial F}{\partial S_t}dW_t$.
So we can write that $u_S=\frac{S_t}{F}\Delta$, for $\Delta=\frac{\partial F}{\partial S_t}$.
Knowing all this, how can I prove the Second Fundamental Theorem of evaluation that says that "A market free of arbitrages is completed if and only if exists one only martingale measure (with numeraire $S_0$)" (Andrea Pascucci - Calcolo stocastico per la finanza - page 86, Th. 3.21)?