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let valid_door_pmf : (door => real) => bool =  
  (pmf) => Real.(
    (pmf(DoorA) + pmf(DoorB) + pmf(DoorC) == 1.0) &&
    (pmf(DoorA) >= 0.0) &&
    (pmf(DoorB) >= 0.0) &&
    (pmf(DoorC) >= 0.0)  
  );

valid_door_pmf(pDoorsEqual)

val valid_door_pmf : (door -> real) -> bool = <fun>
- : bool = true