System I is a proof language for a fragment of propositional logic where isomorphic propositions, such as $A\wedge B$ and $B\wedge A$, or $A\Rightarrow(B\wedge C)$ and $(A\Rightarrow B)\wedge(A\Rightarrow C)$ are made equal. System I enjoys the strong normalization property. This is sufficient to prove the existence of empty types, but not to prove the introduction property (every closed term in normal form is an introduction). Moreover, a severe restriction had to be made on the types of the variables in order to obtain the existence of empty types. We show here that adding $\eta$-expansion rules to System I permits to drop this restriction, and yields a strongly normalizing calculus which enjoys the full introduction property.

翻译：System I是一种适用于命题逻辑片段的证明语言，其中同构命题（如$A\wedge B$与$B\wedge A$，或$A\Rightarrow(B\wedge C)$与$(A\Rightarrow B)\wedge(A\Rightarrow C)$）被视为等价。System I具有强规范化性质。该性质足以证明空类型的存在性，但不足以证明引入性质（每个范式中的封闭项均为引入式）。此外，为获得空类型的存在性，还需对变量的类型施加严格限制。本文证明，向System I添加$\eta$-展开规则可消除这一限制，并得到一个具有完全引入性质的强规范化演算。