A Proof of Coincidence of Labeled Bisimilarity and Observational Equivalence in Applied Pi Calculus

However, this problem can be fixed by requiring active substitutions be defined on the base sort only (see, for instance, [3]). The purpose of this note is to supply a proof for the theorem. In the original semantics in [1], the use of structural equivalence introduces many possibilities and makes it difficult to write a rigorous proof. To overcome the difficulty we shall use intermediate semantics, originally proposed in [3], as a bridge. Four equivalences will be discussed: