Define sets of S C sentences as follows: Γ1={(P →Q1)}, and, for k ≥1, Γk+1=∪{(Qk →Qk+1)} . Then,

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First, let's consider the base case $n=1$. We have $Gamma_1 = {(P rightarrow Q_1)}$. To prove $G

Define sets of $S C$ sentences as follows: $$ \Gamma_1=\left\{\left(P \rightarrow Q_1\right)\right\}, $$ and, for $k \geq 1$, $$ \Gamma_{k+1}=\Gamma_k \cup\left\{\left(Q_k \rightarrow Q_{k+1}\right)\right\} . $$ Then, for any $n \in \mathrm{Nat}^{+}, \Gamma_n \vdash_T\left(P \rightarrow Q_n\right)$.