# Apparent bug in operators using \E

This appears to be a bug: given a spec like

---------------------------- MODULE
EXTENDS Integers

VARIABLE b

InitOp(state) ==  \E v \in 0..1 : (state = v /\ state > 0)

Init == InitOp(b)
Next == (*whatever*)

Spec == Init /\ [][Next]_b /\ WF_b(Next)

===================================

The TLC model checker does not find any initial states. We do get the expected initial state [b=1] if we instead define

InitOp(state) ==  \E v \in 0..1 : (state = v /\ v  > 0)

More generally, if S is some finite set, and Predicate(CHOOSE e \in S : TRUE) is false, the model checker fails to find any initial states with

InitOp(state) == \E v \in S : (state = v /\ Predicate(state))

Furthermore, if
Predicate(CHOOSE e \in S : TRUE) is true, this generates initial states with b equal to every member of S, even those for which Predicate is false.

We get the expected initial states with

InitOp(state) == \E v \in S : (state = v /\ Predicate(v))

(same behavior on Ubuntu, Mac, and Windows)