To formally define the concept, let temporal relation schema R have n time dimensions, Di, i = 1,…, n, and let τi, i = 1,…, n be corresponding timeslice operators, e.g., the valid timeslice and transaction timeslice operators. Then tuples x and y are value equivalent if
∃t1∈D1…∃tn∈Dn(τntn(…(τ1t1(x))…)≠∅) ∧
∃s1∈D1…∃sn∈Dn(τnsn(…(τ1s1(y))…)≠∅)
⇒
τntn(…(τ1t1(x))…) =
τnsn(…(τ1s1(y))…) .
Thus the set of tuples in snapshots of x and the set of tuples in snapshots of y are required to be identical. This is required only when each tuple has some non-empty snapshot.