Conditionally accepted, preprint will be shared shortly
Hypersafety properties of arity $n$ are program properties that relate $n$ traces of a program (or, more generally, traces of $n$ programs). Classic examples include determinism, idempotence, and associativity. A number of relational program logics have been introduced to target this class of properties. Their aim is to construct simpler proofs by capitalizing on structural similarities between the~$n$ related programs. We propose an unexplored, complementary proof principle that establishes hyper-triples (i.e. hypersafety judgments) as a unifying compositional building block for proofs, and we use it to develop a Logic for Hyper-triple Composition (LHC), which supports forms of proof compositionality that were not achievable in previous logics. We prove LHC sound and apply it to a number of challenging examples.