We show that for Multiplicative Exponential Linear Logic (without weakenings)
the syntactical equivalence relation on proofs induced by cut-elimination
coincides with the semantic equivalence relation on proofs induced by the
multiset based relational model: one says that the interpretation in the model
(or the semantics) is injective. We actually prove a stronger result: two
cut-free proofs of the full multiplicative and exponential fragment of linear
logic whose interpretations coincide in the multiset based relational model are
the same "up to the connections between the doors of exponential boxes".Comment: 36 page