# Notation used

If X is an equivalence strategy, a and b are values, and A and B are sets of values, then:

 Notation Definition Description/Note a ∼X b a and b are equivalent under strategy X We also call them X-equivalent. a ∈X B ∃b∈B: a∼Xb Value a is present in B (under X) a ∉X B ¬(a∈XB) ⇔ ¬∃b∈B: a∼Xb Value a is not present in B (under X) A ∩X B { a∈A | a ∈X B } Intersection of A and B under X. [1][2] 1. We could try to define A∩XB also as { a | a∈XA ∧ a∈XB } but this is not quite correct. Such definition would result in infinite set of values, because there are many values that are X-equivalent with any given value. So the set of candidate values must be somehow bound. 2. This also means that ∩X operation is not commutative! In general, A ∩X B can be different from B ∩X A. A -X B { a∈A | a ∉X B } Set difference under X.

When applying delete deltas, a special relation and set operation have to be defined:

 Notation Definition Description/Note a ∼del/X b aid = bid ≠ null ∨ a ∼X b Value a matches deletion pattern b (under X). A -del/X B A - { a∈A | ∃b∈B such that a ∼del b } Result of application of deletion patterns in B to set A (under X).

The aid denotes ID of prism container value a (or null if a is not a prism container value).