Notation
Notation used
If X is an equivalence strategy, a and b are values, and A and B are sets of values, then:
Definition 
Description/Note 

a ∼_{X} b 
a and b are equivalent under strategy X 
We also call them Xequivalent. 
a ∈_{X} B 
∃b∈B: a∼_{X}b 
Value a is present in B (under X) 
a ∉_{X} B 
¬(a∈_{X}B) ⇔ ¬∃b∈B: a∼_{X}b 
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∩_{X}B also as { a  a∈_{X}A ∧ a∈_{X}B } but this is not quite correct. Such definition would result in infinite set of values, because there are many values that are Xequivalent 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 
a_{id} = b_{id} ≠ 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 a_{id} denotes ID of prism container value a (or null if a is not a prism container value).