In TLA+, tuples and sequences are functions. However, unlike in conventional presentations of ZF set theory, functions are not defined as relations (sets of pairs) but are primitive values, axiomatized by
IsAFcn(f) == f = [x \in DOMAIN f > f[x]]
See also Section 16.1.7 of "Specifying Systems".
In particular, << >> = { } is not provable in TLA+, nor is its negation.
Best regards,
Stephan Merz
Sometimes the mathematics behind TLA+ puzzle me. For instance in TLA+ it is possible to prove that ASSUME NEW A PROVE << >> = [ x \in { } > A ] So DOMAIN << >> = { } and << >> is a function. If << >> is a function then << >> is a relation. But if << >> is a function and DOMAIN << >> = { } then << >> = { } But I can't prove << >> = { } with TLA+. Why ?  FL

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